The standard OMG/INCOSE SysML activity diagrams are behavioral models for specifying and analyzing probabilistic systems. In this paper, we present a formal verification framework for these diagrams that helps to mitigate the state-explosion problem in probabilistic model checking. To do so, we propose to reduce the size of SysML activity diagrams by eliminating and merging precise behaviors. The resulting model is checked using Probabilistic Computation Tree Logic (PCTL) properties. Moreover, we present a calculus for SysML activity diagrams (NuAC) that captures their underlying semantics. In addition, we prove the soundness of our approach by defining a probabilistic weak simulation relation between the semantics of the abstract and the concrete models. This relation is shown to preserve the satisfaction of the PCTL properties. Finally, we demonstrate the effectiveness of our approach on an online shopping system case study.