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, 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.