expression: f( y | x ) = P(X= x |Y= y ), it gives the probability that Y takes on the value of y given that X has assumed the value x.
Note: f(Y=2) is the marginal probability of Y; f( x , y ) is the joint probability of X and Y; f( y | x ) is the conditional probability .
eg: if f(Y=2) = 0.27, means the whole probability that Y takes the value of 2 is 0.27 regardless the value X assumed, then f(Y=2|X=5) = 0.53 means the specified probability that Y takes the value of 2 is 0.53, given the X value of 5.