How do you know you are right? These are balance of probability arguments

Most of history ends up boiling down to probability arguments when you dig into it. It's one of the more surprising things as you actually read papers, where far too often you'll see scholars speak with an attitude of certainty around rather spurious evidence. The best tend to make more effort to be conservative with surety.

But between several options of varying probability I don't find it that difficult to identify what I consider very unlikely and what I consider likely.

For example, I rank the idea of people seeing Jesus alive three days after his execution and then watch him float up into the sky extremely unlikely. As many Christians like to point out, we can't be certain it didn't happen, but there's enough reasons why it probably didn't happen that I don't think it did.

You're talking to someone whose personal mantra in life has been Socrates' "All that I know is that I know nothing." Most of existence as far as I'm concerned is probabilities and not certainty, and I value the Epicurean view of entertaining multiple possibilities when it isn't 100% clear which is correct - I think it's a large contributing factor to how they were right about so much.

Within that though, I can look at the two scenarios I presented above and see that one poorly fits the available evidence described and other evidence not described, and the other matches much better, as represented by around five years of a deep dive into the subject matter including discussion and debates with scholars of various perspectives.

of a liar

Likely liars. Paul has a number of characteristics of a narcissist and a habit of swearing he's not lying, and even straight up talks about how he changes what he says depending on the audience. I wouldn't trust him more than you could throw him, and maybe not even that much (he was allegedly smallish).

The gospel of Mark is also likely propagating lies, whether of original invention or secondhand inheritance.

Then Luke and potentially Mark have possible redactional layers which are further lying about things (like a 180° on not taking people's money).

Matthew is probably worst of all with the outright lying, and evidentially had extra-cannonical resources in front of him that he was copying from and then making up secret explanations for while in general promoting a tradition of secret teachings (I think it may have come from an ex-Essene community).

John takes what I do think was some rudimentary earlier resource and then actively works to subvert and conceal the origin of that resource with what are likely additional lies, that span at least two redactional layers.

Later on people forge letters from Paul and Peter.

There's quite a lot of liars involved in forming what we have.

But the thing with liars is that while you can't trust their positive statements, they tend to reflect more trustworthy things in what they oppose or accidentally acknowledge. You kind of have to treat them like a hostile witness in a court case.

So for example with Mark, one of the most basic ways this manifests is the aforementioned public/private pattern. While I wouldn't believe what Mark talks about occurring in public that supports his agenda or theology like a faith healing or Jesus telling people marriage is between a man and a woman (anachronistic relevance before Nero married two men in the 60s making same sex marriage an institution in the Roman empire), I tend to think the things it sets up as taking place in public before it immediately tries to contextualize them in a different direction with private explanations are one way to detect things that were part of an earlier commonly known record.

It's tough work necessitating different approaches and maybe at best there's about 3-4% of the material in there that I'd confidently label as preceding Mark's earliest redactional layer.

You mention Mark borrowing from Greek thinkers and while probably true does nothing to prove a historical Jesus.

Not Mark. Mark is oblivious to Greek thought, which is why it's interesting. The Greek/Roman philosophical influence is very pronounced in Thomas, it is present in things discussed with the Christian community in Corinth, but it isn't in Mark other than in a vestigial way.

And the specific ways it's phrased in places in Thomas combines Greek/Roman philosophy with the phrasing and metaphors of prophets in the Old Testament. I'd be very surprised if that core work was from someone who wasn't familiar with both.

So while no, I can't be for sure that a historical Jesus existed, I am pretty confident that someone familiar with both Lucretius, Plato, and Hebrew texts composed a number of sayings which ended up attributed to a Jesus in the first century when he was a relative nobody, at least one of which was likely composed during Pilate's reign, several of which predated Paul, several more of which predated Mark, more of which predated Luke, and more of which predated Matthew. All of which ended up inside the 3rd-4th century only surviving copy of the Gospel of Thomas alongside additional sayings that were composed or taken from canonical texts later on.

To elegantly tie together Plato and Lucretius occasionally using language and metaphors from the OT in the first century seems like a pretty difficult task. It strikes me as bizarre that the person undertaking this Herculean accomplishment would then turn around and attribute it all to a relative nobody from a small cultic tradition who was allegedly executed by the Roman empire at its peak and whose adherents were actively being persecuted by the religious theocracy in Judea before being subverted by a growing splinter tradition largely owing itself to one of the people known to be persecuting them.

Maybe a better fitting version of events is that there really was a historical nobody who combined these things, pissed off the religious theocracy he was under with the conclusions he came to which undermined their authority such that he was killed by the state as soon as it was possible to justify it, then his followers and teachings were actively persecuted in areas the religious theocracy had authority while being actively subverted with a different version of fictionalized events and interpretations in the areas they didn't have authority so they could bring it all back closer to conservative Judaism and funnel money and resources back to themselves - and then that subversion attempt was so unexpectedly successful that now a third of the world population believes it today.