This conversation piqued my interest because one of my expectations was subverted. Due to habits ingrained in me while applying Bayes' theorem in more formal statistical inference, I almost never give consideration to P(B) in these informal applications; I find it much easier to think about the likelihood ratio, P(B given A) / P(B given not-A).

Given P(A), the likelihood ratio determines P(B) and vice versa, so it's not like there's any difference in practice. But I find it interesting to observe a different habit of mind in action.