I think you may have your conditional probabilities backward? P(research-related|origin-place) and P(natural|origin-place) do sum to one, since those are mutual

I think you may have your conditional probabilities backward? P(research-related|origin-place) and P(natural|origin-place) do sum to one, since those are mutually exclusive and exhaustive outcomes. P(origin-place|research-related) and P(origin-place|natural) don't, though. For example, if "origin-place" is "anywhere in the universe", then they're both exactly equal to one, so they sum to two. If it's "Mars", then they're both approximately zero. The virology institute (again, not just any virology institute; the single largest collection of novel related viruses in the world by far) doesn't decrease the probability of natural pandemics. It increases the probability of research-related pandemics, so natural becomes a smaller fraction of that larger total.