We shall clarify the role that backward solutions play in computing absorption probabilities and in the model-checking of stochastic logics as CSL and CSLTA, which typically require the steady state solution of a non-ergodic CTMC and MRP respectively. Moreover we show that the algorithm for the computation of the whole set of states that satisfy a CSL formula, which is standard practice in CSL model-checkers, can be seen as a case of computation of backward probabilities of Continuous Time Markov Chains (CTMCs). The backward computation of MRP is then inserted in the context of matrix-free solution technique, which allows to deal with MRP of much bigger size than the standard approach based on the computation and solution of the embedded Markov chain.