We could change the model to not have any implicit assumption about location. Then instead of dividing by the population of China, we'd divide by the world population. The result should be the same, assuming we appropriately adjust our prior probability P(virus from WIV) to account for the fact that there are more BSL-4 facilities worldwide than in China.
P(Came from WIV|Global Epidemic starts in Wuhan) ~= 97%
However, P(Started Near a BSL Rated facility|Global Epidemic) is also high (not going to estimate it).
But you have assumed that P(Global Epidemic starts in Wuhan) = 1; which is not true. P(Global Epidemic starts in Wuhan) is probably quite low and they got unlucky because it had to start somewhere. In this context, that assumption is tantamount to flipping a coin then saying "P(Heads) = 1". It isn't, P(Head) = 0.5 but it does happen sometimes.
If we assume P(Global Epidemic starts in Wuhan) = 1 (because it did happen) then P(Came from WIV) is either 0 or 1, because it either did or didn't happen in the same way that the virus started in Wuhan.
The best I can come up with is that probability is very sensitive to what you assume is happening to generate results. In this case, you're assuming that the WIV in particular is important which I suspect links the pandemic implicitly to Wuhan. That isn't a math error, but it is not going to give you a useful result.
This isn't an error of logic so much as an error in scenario construction - it is ignoring possibility that the virus appeared near a random BSL rated facility, which is probably very high since a new virus would likely be detected first in dense urban centers where that sort of infrastructure tends to be. If the virus is likely to appear near a BSL facility, then the fact it appeared near a specific BSL facility shouldn't be leading you to the sort of answer you got.
That probability is only 1 in hindsight, where the probability of everything is 1 because it has already happened. In foresight the probability was not 1. And whatever city the virus started in was going to have a BSL-2+ facility studying infectious diseases. I'm probably sitting within 2-4km of a BSL-3 facility studying infectious diseases as I type this, because I am in a city.
The fast that WIV is BSL-4 is significant, but it isn't going to get you to 97%. Even 75% is high. Particularly if WIV is located where it is because there are good local sources of coronaviruses to study.