Understanding crowd behaviors in a large social event is crucial for event management. Passive WiFi sensing, by collecting WiFi probe requests sent from mobile devices, provides a better way to monitor crowds compared with people counters and cameras in terms of free interference, larger coverage, lower cost, and more information on people's movement. In existing studies, however, not enough attention has been paid to the thorough analysis and mining of collected data. Especially, the power of machine learning has not been fully exploited. In this paper, therefore, we propose a comprehensive data analysis framework to fully analyze the collected probe requests to extract three types of patterns related to crowd behaviors in a large social event, with the help of statistics, visualization, and unsupervised machine learning. First, trajectories of the mobile devices are extracted from probe requests and analyzed to reveal the spatial patterns of the crowds' movement. Hierarchical agglomerative clustering is adopted to find the interconnections between different locations. Next, k-means and k-shape clustering algorithms are applied to extract temporal visiting patterns of the crowds by days and locations, respectively. Finally, by combining with time, trajectories are transformed into spatiotemporal patterns, which reveal how trajectory duration changes over the length and how the overall trends of crowd movement change over time. The proposed data analysis framework is fully demonstrated using real-world data collected in a large social event. Results show that one can extract comprehensive patterns from data collected by a network of passive WiFi sensors.