Transferring representational knowledge of a model to another is a wide-ranging topic in machine learning. Those applications include the distillation of a large supervised or self-supervised teacher model to a smaller student model or self-supervised learning via self-distillation. Knowledge distillation is an original method to solve these problems, which minimizes a cross-entropy loss between the prototypical probabilistic outputs of teacher and student networks. On the other hand, contrastive learning has shown its competency in transferring representations as they allow students to capture the information of teacher representations. In this paper, we amalgamate the advantages of knowledge distillation and contrastive learning by modeling the critic of a contrastive objective by the prototypical probabilistic discrepancy between two features. We refer to it as prototypical contrastive predictive coding and present efficient implementation using the proposed objective for three distillation tasks: supervised model compression, self-supervised model compression, and self-supervised learning via self-distillation. Through extensive experiments, we validate the effectiveness of our method and show that our method achieves state-of-the-art performance in supervised / self-supervised model compression.