The conditional entropy measures how much entropy a random variable X has remaining if we have already learned the value of a second random variable Y. It is referred to as the entropy of X conditional on Y, and is written H(X | Y). 
If the probability that X = x is denoted by p(x), then we donote by p(x | y) the probability
that X = x, given that we already know that Y = y. p(x | y) is a conditional probability.
In Baysian language, Y represents our prior information information about X.
The conditional entropy is just the Shannon entropy with p(x | y) replacing p(x), and then we average it over all possible "Y".
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Using the Baysian sum rule p(xy) = p(x | y)p(y), one finds that the conditional entropy is equal to
with "H(XY)" the joint entropy of "X" and "Y".
