In this paper, the vector generalization of the Wardrop equilibrium principle is briefly discussed, and a new definition of vector equilibrium in the functional setting of Lebesgue spaces endowed with a probability measure is proposed. The relationship between vector variational inequalities and vector equilibrium in the probabilistic setting is shown to be of the same kind as in the deterministic case, and to confirm that vector variational inequalities can only provide a subclass of solutions of vector equilibrium problems. The results proposed in this paper are new and interesting.