In this paper, we propose a probabilistic framework targeting three important issues in the computation of quality and trust in decentralized systems. Specifically, our approach addresses the multi-dimensionality of quality and trust, taking into account credibility of the collected data sources for more reliable estimates, while also enabling the personalization of the computation. We use graphical models to represent peers' qualitative behaviors and exploit appropriate probabilistic learning and inference algorithms to evaluate their quality and trustworthiness based on related reports. Our implementation of the framework introduces the most typical quality models, uses the Expectation-Maximization algorithm to learn their parameters, and applies the Junction Tree algorithm to inference on them for the estimation of quality and trust. The experimental results validate the advantages of our approach: first, using an appropriate personalized quality model, our computational framework can produce good estimates, even with a sparse and incomplete recommendation data set; second, the output of our solution has well-defined semantics and useful meanings for many purposes; third, the framework is scalable in terms of performance, computation, and communication cost. Furthermore, our solution can be shown as a generalization or serve as the theoretical basis of many existing trust computational approaches.