Bayes' Rule

p(X=xY=y)=p(X=x,Y=y)p(Y=y)=p(X=x)p(Y=yX=x)xp(X=x)p(Y=yX=x)p(X=x|Y=y) = \frac{p(X=x, Y=y)}{p(Y=y)} = \frac{p(X=x)p(Y=y|X=x)}{\sum_{x'}{p(X=x')p(Y=y|X=x')}}