Resilience is a property of major interest for the design and analysis of generic complex systems. A system is resilient if it can adjust in response to disruptive shocks, and still provide the services it was designed for, without interruptions. In this work, we adapt a formal definition of resilience for constraint-based systems to a probabilistic framework derived from hidden Markov models. This allows us to more realistically model the stochastic evolution and partial observability of many complex real-world environments. Within this framework, we propose an efficient and exact algorithm for the inference queries required to construct generic property checking. We show that the time complexity of this algorithm is on par with other state-of-the-art inference queries for similar frameworks (that is, linear with respect to the time horizon). We also provide considerations on the specific complexity of the probabilistic checking of resilience and its connected properties, with particular focus on resistance. To demonstrate the flexibility of our approach and to evaluate its performance, we examine it in four qualitative and quantitative example scenarios: (1) disaster management and damage assessment; (2) macroeconomics; (3) self-aware, reconfigurable computing for aerospace applications; and (4) connectivity maintenance in robotic swarms.