The reachability analysis problem of Max Plus Linear (MPL) systems has been properly solved using the Difference-Bound Matrices approach. In this work, the same approach is considered in order to solve the reachability analysis problem of MPL systems subjected to bounded noise, disturbances and/or modeling errors, called uncertain MPL (uMPL) systems. Moreover, using the results on the reachability analysis of uMPL systems, we solve the conditional reachability problem, herein defined as the support calculation of the probability density function involved in the stochastic filtering problem.