As someone that makes forecasts for a living, I'd like to see what you're assumptions are about the base rates there.
As for how the facts produce modifications to the base rate, personally I think that a virus identified in a cave over a thousand miles away popping up in a very urban area right next to a BSL facility that specializes in researching that type of virus moves the needle toward it being more likely a lab escape. You seem to feel otherwise and I don't really agree. In particular, if you take the converse: suppose the virus wasn't known at all to man, you'd probably argue it also pushes you toward the conclusion that it was a natural spillover. (In which case, I'd be in agreement.) So I don't think that argument is really a logical one.
Your objection in the last paragraph, describing this as a "bioweapon modified virus" is really a classic strawman, and since it isn't the argument I was making I see no reason to indulge it. It is indeed a relatively ridiculous notion.
Also, just for precision, my own assessment of the truth value there is about 70% in favor of a lab-leak.
In the last few decades there have been 1-2 confirmed lab leaks per year. And they're often thing like "we found a vial of smallpox we didn't know we had" not new diseases.
Nature very capably produced colds, flus, a bunch of nasty diarrhoeal diseases, the many and varied sexually transmitted diseases, the hemorrhagic fevers, and so on. For "some new disease variant that I don't know anything about", my prior would be more like 1/99 lab leak to natural origin.
We have known about coronaviruses for almost 100 years, and we have been studying them due to their dangers for atleast 60 years, and it has likely existed since before humans could be called human. And it has been shown to be a highly virulent numerous times in many different forms. No matter how low the chances of winning the lottery, when literally billions of people are playing it daily, it is only of matter of when, not if, it turns into something more dangerous.
Now none of that comes anywhere near proving anything, but the fact that we have had multiple coronavirus infections in the past, many of which have come dangerously close to pandemic level infections, makes a natural occurrence seem the most likely source.
On top of all that, even if it did come from a lab, why does that matter? A handful of extra lottery tickets were sold and someone won from that pool. This isn't some bioweapon modified virus purposefully bred from a farm of human subjects, you would never be able to get away with such a program in a large publicly known virology lab and we aren't knowledgeable enough in viral genetics to make something like that without testing it on farms of people. There are no markers indicating engineering it in any way that we are actually capable of. And worst case it is something a mere handful of unguided generations away from a sample that was pulled from the public already and the lab got "lucky" with a random mutation on a petri dish they were studying.