The temporal logics LTLf+ and PPLTL+ have recently been introduced to express objectives over infinite traces. These logics are appealing because they match the expressive power of LTL on infinite traces while enabling efficient DFA-based techniques, which have been crucial to the scalability of reactive synthesis and adversarial planning in LTLf and PPLTL over finite traces. In this paper, we demonstrate that these logics are also highly effective in the context of MDPs. Introducing a technique tailored for probabilistic systems, we leverage the benefits of efficient DFA-based methods and compositionality. This approach is simpler than its nonprobabilistic counterparts in reactive synthesis and adversarial planning, as it accommodates a controlled form of nondeterminism ("good for MDPs") in the automata when transitioning from finite to infinite traces. Notably, by exploiting compositionality, our solution is both implementation-friendly and well-suited for straightforward symbolic implementations.