The purpose of the present paper is
to introduce two notions of conditional entropy
of a finite commutative hypergroup $\mathcal{K}$,
one of which is associated with the normalized Haar measure of
$\mathcal{K}$ and the other is associated with the canonical
state of $M^b({\mathcal{K}})$ which is a $*$-algebra consisted
of all measures on $\mathcal{K}$.
For a subhypergroup or
a generalized orbital hypergroup,
the dual relations of these conditional entropy are discussed.
Moreover, it is shown that the structures of hypergroups are
characterized by these entropy.