In [16] K. Menger proposed the probabilistic concept of distance by replacing the number $d(p,q)$, as the distance between points $p,q$, by a distribution function $F_{p,q}$. This idea led to development of probabilistic analysis [3, 11, 18]. In this paper, generalized probabilistic 2-normed spaces are studied and topological properties of these spaces are given. As an example, a space of random variables is considered, connections with the generalized deterministic 2-normed spaces studied in [14] being also given.