Intelligent autonomous agents need to reason about different kinds of uncertainty in a Multi-Agent System (MAS): first, due to the occurrence of randomization and, second, their inability to completely observe the state of the system. In this paper, we investigate the verification of system specifications in probabilistic variants of the logics ATL and ATL∗ under imperfect information (II). The resulting setting combines these two sources of uncertainty and captures the situation in which agents have qualitative uncertainty about the local state as well as quantitative uncertainty about the occurrence of future events. Since the model-checking problem is undecidable when considered in the context of strategies with perfect recall, we focus on memoryless (positional) strategies. As the main result, we show that, in stochastic MAS under II, model-checking Probabilistic ATL is in EXPTIME when agents play probabilistic strategies. Filling the gap in recent work, we also show that model-checking Probabilistic ATL∗ is PSPACE-complete when the proponent coalition is restricted to deterministic strategies.