In a Bayesian network, a probabilistic inference is the procedure of computing the posterior probability of query variables given a collection of evidences. In this paper, we propose an algorithm that efficiently carries out the inferences whose query variables and evidence variables are restricted to a subset of the set of the variables in a BN. The algorithm successfully combines the advantages of two popular inference algorithms — variable elimination and clique tree propagation. We empirically demonstrate its computational efficiency in an affective computing domain.