Interesting, but wrong use of conditional probabilities. All OP is saying is that the frequency of people from school x following topic y is p. The dataset is

Interesting, but wrong use of conditional probabilities. All OP is saying is that the frequency of people from school x following topic y is p. The dataset is just not the right one to say that P(x|y) = p, because of, say, all the people who follow food in NYC and go to NYU which were not taken into account here.