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.

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.