Bayes' Theorem Application Question
I'm reading Networks by Mark Newman and I'm confused about one of his applications of Bayes' theorem. He begins with the following equation:
He then assumes the prior probabilities P(x) and P(y) are uniform and therefore constants. He then states that we cannot assume the same for P(A) and introduces the following as its prior probability (where p is another probability on which A depends)
From this he updates the formula above as follows:
Why doesn't P(data|A,x,y) include p (and why did he introduce p into the posterior probability)?