We present a formalization of Probabilistic Timed Automata (PTA) for which we try to follow the formula ``MDP + TA = PTA'' as far as possible: our work starts from existing formalizations of Markov Decision Processes (MDP) and Timed Automata (TA) and combines them modularly. We prove the fundamental result for Probabilistic Timed Automata: the region construction that is known from Timed Automata carries over to the probabilistic setting. In particular, this allows us to prove that minimum and maximum reachability probabilities can be computed via a reduction to MDP model checking, including the case where one wants to disregard unrealizable behavior.