The verification of systems for protecting sensitive and confidential information is becoming an increasingly important issue. Differential privacy is a promising notion of privacy originated from the community of statistical databases, and now widely adopted in various models of computation. We consider a probabilistic process calculus as a specification formalism for concurrent systems, and we propose a framework for reasoning about the degree of differential privacy provided by such systems. In particular, we investigate the preservation of the degree of privacy under composition via the various operators. We illustrate our idea by proving an anonymity-preservation property for a variant of the Crowds protocol for which the standard analyses from the literature are inapplicable. Finally, we make some preliminary steps towards automatically computing the degree of privacy of a system in a compositional way.