We consider paths in weighted and directed temporal networks, introducing
tools to compute sets of paths of high probability. We quantify the relative
importance of the most probable path between two nodes with respect to the
whole set of paths, and to a subset of highly probable paths which incorporate
most of the connection probability. These concepts are used to provide
alternative definitions of betweenness centrality. We apply our formalism to a
transport network describing surface flow in the Mediterranean sea. Despite the
full transport dynamics is described by a very large number of paths we find
that, for realistic time scales, only a very small subset of high probability
paths (or even a single most probable one) is enough to characterize global
connectivity properties of the network