This work deals with the problem of strategic path planning while avoiding detection by a mobile adversary. In this problem, an evading agent is placed on a graph, where one or more nodes are defined as safehouses. The agent's goal is to find a path from its current location to a safehouse, while minimizing the probability of meeting a mobile adversarial agent at a node along its path (i.e., being captured). We examine several models of this problem, where each one has different assumptions on what the agents know about their opponent, all using a framework for computing node utility. We use several risk attitudes for computing the utility values, whose impact on the actual performance of the path planning algorithms is highlighted by an empirical analysis. Furthermore, we allow the agents to use information gained along their movement, in order to efficiently update their motion strategies on-the-fly. Analytic and empiric analysis show that on-the-fly updates increase the probability that our agent reaches its destination safely.