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.