We address the class of probabilistic planning problems where the objective is to maximize the probability of reaching a prescribed goal. The complexity of probabilistic planning problems makes it difficult to compute high quality solutions for large instances, and existing algorithms either do not scale, or do so at the expense of the solution quality. We leverage core similarities between probabilistic and fully observable non-deterministic (FOND) planning to construct a sound, offline probabilistic planner, ProbPRP, that exploits algorithmic advances from state-of-the-art FOND planner, PRP, to compute compact policies that are guaranteed to bypass avoidable deadends. We evaluate ProbPRP on a selection of benchmarks used in past probabilistic planning competitions. The results show that ProbPRP, in many cases, outperforms the state of the art, computing substantially more robust policies and at times doing so orders of magnitude faster.