Y again given Z but again the bottom here doesn't really matter much in baseball we usually know that we just need to compute the top part for every possible value of x and once we computed the top part for every value of x we can see what it sums to and whatever it sums to is what goes in the bottom right and so applying Bayes rule is about doing this for all X and then summing to know what the bottom is and so here we see that we can incorporate new evidence we already had evidence we had already had X given Z we had a past observation