It is useful and necessary to talk about conditional entropy, instead of leaving the subject where the textbook drops off. Let $Y$ be the set of labels, and let $X$ be the set of features.

Conditional Entropy We now define conditional entropy as $H(Y \mid X=x) = -\sum_{y\in Y} \Pr(Y=y)\log \Pr(Y=y \mid X=x)$.

We interpret the conditional entropy as the variability in the label, given the feature $X=x$. In context: how uncertain are we about a person’s health, given that we know how many times a year they go to the doctors office.