Ah, insightful! I hadn't seen forms of Bayes' Rule other than the probability form before today, and this is very helpful (well, perhaps I had seen them but it hasn't "hit me" until now).
I like that this is emphasized. To further emphasize, I think a formula should be added as a block level element underneath.
I think it'd be clearer to have two different headers. The way it's set up right now, I didn't initially see that this one article is talking about two different (but related) approaches.
I think I'd find it easier to understand if we were talking about something more concrete, like strep throat.
I, in general, think things are clearer when real world examples like this are given in the beginning, rather than after the abstract explanation. I think most people find the same thing.