  Cops and Robbers games have been studied for the last few decades in computer
science and mathematics. As in general pursuit evasion games, pursuers (cops)
seek to capture evaders (robbers); however, players move in turn and are
constrained to move on a discrete structure, usually a graph, and know the
exact location of their opponent. In 2017, Bonato and MacGillivray presented a
general characterization of Cops and Robbers games in order for them to be
globally studied. However, their model doesn't cover cases where stochastic
events may occur, such as the robbers moving in a random fashion. In this paper
we present a novel model with stochastic elements that we call a Generalized
Probabilistic Cops and Robbers game (GPCR). A typical such game is one where
the robber moves according to a probabilistic distribution, either because she
is rather lost or drunk than evading, or because she is a robot. We present
results to solve GPCR games, thus enabling one to study properties relating to
the optimal strategies in large classes of Cops and Robbers games. Some classic
Cops and Robbers games properties are also extended.
