A "path-based sensor" produces a single observation along a continuous path. For example, a boolean path-based sensor returns a single "1" if an event of interest is detected at any point along the path and a "0" otherwise. Notably, a "1" provides no direct information about where along the path the event(s) may have occurred. Previous work has demonstrated that observations from multiple path-based sensors can be fused to create a Bayesian belief map over the spatial locations of the underlying event or phenomenon. Moreover, path planning can employ Shannon information theory to accelerate the rate of convergence of the belief map. In this paper, we present a new method to update the belief map based on a path-based sensor observation, and then plan paths to increase information gain. In contrast to prior work that approximates the posterior by averaging over the alternative event histories, we introduce a Bayesian Network (BN) formulation that models the probabilistic relationships between the latent variables and path-based sensor measurements, enabling a more principled Bayesian belief update. We consider static hazard detection in a communication-denied environment as a representative problem setting. The event of a robot returning from its path corresponds to a path-based hazard sensor reading of "0" (hazard not detected), while a robot failing to return corresponds to a reading of "1" (hazard detected). We consider false positives and false negatives. We find that the new method leads to quicker convergence of the belief map than prior work in both single- and multi-robot cases.