Continuing our preleminary work \cite{knowles14}, we define the safest-with-sight pathfinding problems and explore its solution using techniques borrowed from measure-theoretic probability theory. We find a simple recursive definition for the probability that an ideal pathfinder will select an edge in a given scenario of an uncertain network where edges have probabilities of failure and vertices provide "vision" of edges via lines-of-sight. We propose an approximate solution based on our theoretical findings that would borrow techniques from approximate dynamic programming.