End-to-end models are favored in automatic speech recognition (ASR) because of their simplified system structure and superior performance. Among these models, Transformer and Conformer have achieved state-of-the-art recognition accuracy in which self-attention plays a vital role in capturing important global information. However, the time and memory complexity of self-attention increases squarely with the length of the sentence. In this paper, a prob-sparse self-attention mechanism is introduced into Conformer to sparse the computing process of self-attention in order to accelerate inference speed and reduce space consumption. Specifically, we adopt a Kullback-Leibler divergence based sparsity measurement for each query to decide whether we compute the attention function on this query. By using the prob-sparse attention mechanism, we achieve impressively 8% to 45% inference speed-up and 15% to 45% memory usage reduction of the self-attention module of Conformer Transducer while maintaining the same level of error rate.