Unsupervised video anomaly detection (UVAD) aims to detect abnormal events in videos without any annotations. It remains challenging because anomalies are rare, diverse, and usually not well-defined. Existing UVAD methods are purely data-driven and perform unsupervised learning by identifying various abnormal patterns in videos. Since these methods largely rely on the feature representation and data distribution, they can only learn salient anomalies that are substantially different from normal events but ignore the less distinct ones. To address this challenge, this paper pursues a different approach that leverages data-irrelevant prior knowledge about normal and abnormal events for UVAD. We first propose a new normality prior for UVAD, suggesting that the start and end of a video are predominantly normal. We then propose normality propagation, which propagates normal knowledge based on relationships between video snippets to estimate the normal magnitudes of unlabeled snippets. Finally, unsupervised learning of abnormal detection is performed based on the propagated labels and a new loss re-weighting method. These components are complementary to normality propagation and mitigate the negative impact of incorrectly propagated labels. Extensive experiments on the ShanghaiTech and UCF-Crime benchmarks demonstrate the superior performance of our method. We plan to make the code and trained models publicly available.