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This paper presents a framework for path planning over probabilistic costmaps of outdoor terrain that is compatible with fast grid-based planners such as A* and D*. We begin with an exemplar of how probabilistic costmaps may be constructed and then show how the a priori availability of such maps lends itself to the precomputation of exact probabilistic heuristics. In turn, the probabilistic nature of these heuristics allow the user to employ a bounded speed-accuracy tradeoff that characterizes the risk of paths returned not being of optimal shortest-path length. Results are shown which demonstrate that the method is able to closely approximate a probability distribution over the underlying exact distance and that efficiency increases on the order of 90% in terms of nodes expanded, and 60% in terms of search time over Euclidean distance heuristics, can be achieved.