  To a finitely generated profinite group $G$, a formal Dirichlet series
$P_G(s)=\sum_{n \in \mathbb N} {a_n(G)}/{n^s}$ is associated, where
$a_n(G)=\sum_{|G:H|=n}\mu(H, G)$ and $\mu(H,G)$ denotes the M\"obius function
of the lattice of open subgroups of $G.$ Its formal inverse $P_G^{-1}(s)$ is
the probabilistic zeta function of $G$. When $G$ is prosoluble, every
coefficient of $(P_G(s))^{-1}$ is nonnegative. In this paper we discuss the
general case and we produce % existence of a non-prosoluble example and We
construct a non-prosoluble finitely generated group $G$ with the same property.
