The Dempster-Shafer (D-S) theory of evidence suggests a coherent approach to aggregate evidence bearing on groups of mutually exclusive hypotheses; however, the uncertain relationships between evidence and hypotheses are difficult to represent in applications of the theory. In this paper, we extend the multivalued mapping in the D-S theory to a probabilistic one that uses conditional probabilities to express the uncertain associations. In addition, Dempster’s rule is used to combine belief update rather than absolute belief to obtain results consistent with Bayes’ theorem. The combined belief intervals form probability bounds under two conditional independence assumptions. Our model can be applied to expert systems that contain sets of mutually exclusive and exhaustive hypotheses, which may or may not form hierarchies.