  The Fisher's information metric is introduced in order to find the real
meaning of the probability distribution in classical and quantum systems
described by Riemaniann non-degenerated superspaces. In particular, the
physical r\^{o}le played by the coefficients $\mathbf{a}$ and $\mathbf{a}^\ast$
of the pure fermionic part of a genuine emergent metric solution, obtained in
previous work is explored. To this end, two characteristic viable distribution
functions are used as input in the Fisher definition: first, a Lagrangian
generalization of the Hitchin Yang-Mills prescription and, second, the
probability current associated to the emergent non-degenerate superspace
geometry. Explicitly, we have found that the metric solution of the superspace
allows establish a connexion between the Fisher metric and its quantum
counterpart, corroborating early conjectures by Caianiello {\em et al.} This
quantum mechanical extension of the Fisher metric is described by the $CP^1$
structure of the Fubini-Study metric, with coordinates $\mathbf{a}$ and
$\mathbf{a}^\ast$.
