Tweet clustering for event detection is a powerful modern method to automate the real-time detection of events. In this work we present a new tweet clustering approach, using a probabilistic approach to incorporate temporal information. By analysing the distribution of time gaps between tweets we show that the gaps between pairs of related tweets exhibit exponential decay, whereas the gaps between unrelated tweets are approximately uniform. Guided by this insight, we use probabilistic arguments to estimate the likelihood that a pair of tweets are related, and build an improved clustering method. Our method Social Media Event Response Clustering (SMERC) creates clusters of tweets based on their tendency to be related to a single event. We evaluate our method at three levels: through traditional event prediction from tweet clustering, by measuring the improvement in quality of clusters created, and also comparing the clustering precision and recall with other methods. By applying SMERC to tweets collected during a number of sporting events, we demonstrate that incorporating temporal information leads to state of the art clustering performance.