Random probability vectors are of great interest especially in view of their application to statistical inference. Indeed, they can be used for determining the de Finetti mixing measure in the representation of the law of a partially exchangeable array of random elements taking values in a separable and complete metric space. In this paper we describe a construction of a vector of Dirichlet processes based on the normalization of completely random measures that are jointly infinitely divisible. After deducing the form of the Laplace exponent of the vector of the gamma completely random measures, we study some of their distributional properties. Our attention particularly focuses on the dependence structure and the specific partition probability function induced by the proposed vector.