With the widespread success of deep neural networks in science and technology, it is becoming increasingly important to quantify the uncertainty of the predictions produced by deep learning. In this paper, we introduce a new method that attaches an explicit uncertainty statement to the probabilities of classification using deep neural networks. Precisely, we view that the classification probabilities are sampled from an unknown distribution, and we propose to learn this distribution through the Dirichlet mixture that is flexible enough for approximating any continuous distribution on the simplex. We then construct credible intervals from the learned distribution to assess the uncertainty of the classification probabilities. Our approach is easy to implement, computationally efficient, and can be coupled with any deep neural network architecture. Our method leverages the crucial observation that, in many classification applications such as medical diagnosis, more than one class labels are available for each observational unit. We demonstrate the usefulness of our approach through simulations and a real data example.