Context and implications
Existence of divinity is an extremely important claim, it requires a huge amount of evidence. I can accept that Julius Caesar did this and said that with fairly large margins of error. The reason I can is that it really doesn't matter to me. Historical evidence of a deity and especially the link of one person to said deity is a really important question. If such a deity is real, I need to profoundly change my behaviour; it's not something I am going to accept without very certain evidence. In other words, I am sticking to my null hypothesis because of the huge implications of the tested hypothesis. At this point, you may feel an urge to tell me that this makes me evil, as if I am somehow avoiding God. I can demonstrate the circular nature of this with two arguments. Firstly, imagine you tell me that by jumping off a cliff I will achieve eternal happiness and life. In this case, the consequences under my current theory (no belief in any such supernatural mechanisms) are dire. I would need stupendous amounts of evidence to convince myself to do it. It is the same for religion, it will literally change the way I live, that's a big deal. Secondly, you would exercise the same caution when evaluating other religions and their books, and you would implore me to do the same if I was to look at the historicity of Muhammed. If you are compelled to reply to that with, "I have looked at Islam, and it really was silly and unbelievable", just seriously consider whether perhaps your cultural or confirmation biases would have affected your judgement at all. For more about my choice of the null hypothesis, read this post.
Bayes' Theorem
One qualitative assessment of Bayes' theorem is the need to consider prior evidence. If you'd rolled a dice 1000 times and every time it came up a one, and a friend told you that your next roll would be a six, you should be a little skeptical. You would also be skeptical of a historical document which talked about unicorns and dragons, because you have never observed any yourself. This is not unreasonable, the claim is extraordinary, and to quote Sagan: "extraordinary claims require extraordinary evidence". If a historical document said that people generally went about doing normal peoplely things in the past, we'd be much less critical of it. It is not wrong to "view" the bible in such terms, it is indeed correct to require extraordinary evidence for the claims of miracles and of deity.
To use a further example: if you found a video of me shooting a laser out of my mouth, would you believe I possessed a power like some kind of gastronomical Cyclops? No, you would view the evidence in light of what you know about me, and about the source. You've never seen anyone shoot lasers out of their mouths, and you'd probably be right to say it's impossible within our current understanding of physics. Furthermore, you know that videos are easily and convincingly faked. It would be ridiculous and naive to believe I could. Of course, with the bible it is not so obvious, but think about the concepts which would lead you to reject or accept such claims.
Were they lying?
I was asked several times whether or not I thought the gospels were faked. I see this as a false dichotomy, on one end the early church conspired to mislead us and on the other, the whole bible is literally (like literally literally) true. In reality, humans are capable of everything from outright lies to honesty, but there's a lot in between where intentions are good but the outcomes are false. Biblical experts widely agree that none of the gospels were written by eye witnesses. It is perfectly plausible that the facts about Jesus were escalated, getting more and more fanciful as traditions began to form and people began to get caught up in this new messiah. Like a game of Chinese whispers, an increasingly fascinating story on top of someone who was probably a great teacher. Naturally, the accounts may all be true, but it is most certainly a large leap to suggest that it amounts to evidence. It is circular at best: there is a plausible pathway to the gospels being formed and not being literally true.
But how did a lie convince so many people? They plead. As people we are bombarded with huge amount of information from birth. Much of what we learn is simply copied and pasted from our culture and parents. Once a religion takes hold, it stays, and as I have mentioned before, strong religions remain. By definition. The weak religions die much more easily so the only ones that are left are the convincing ones. Obviously this is a theory, but it shows that there is a possible mechanism for convincing religions to form without any real truth behind them. Also, this argument falls apart when we consider other religions. How about Islam vs Christianity, both religions deny the authenticity of the other. Clearly convincing incorrect religions can form, convincing in fact to 2.2billion and 3.3billion respectively. People don't tend to lie, they bend facts with a whole slew of biases. Humans are really terrible sources for many reasons, especially in a religiously and emotionally charged environment.