AbstractThis paper considers Stochastic Shortest Path (SSP) problems in probabilistic networks. A variety of approaches have already been proposed in the literature. However, unlike in the deterministic case, they are related to distinct models, interpretations and applications. We have chosen to look at the case where detours from the original path must be taken whenever the “first‐choice” arc fails. The main results obtained include the proof of some counterintuitive facts (e.g., the SSP may contain a cycle), the proof of the validity of applying stochastic programming to this problem and the proof that the computational complexity of a particular SSP problem is polynomial.