  We provide a stochastic extension of the Baez-Fritz-Leinster characterization
of the Shannon information loss associated with a measure-preserving function.
This recovers the conditional entropy and a closely related
information-theoretic measure that we call conditional information loss.
Although not functorial, these information measures are semi-functorial, a
concept we introduce that is definable in any Markov category. We also
introduce the notion of an entropic Bayes' rule for information measures, and
we provide a characterization of conditional entropy in terms of this rule.
