Social media has now become the de facto information source on real world events. The challenge, however, due to the high volume and velocity nature of social media streams, is in how to follow all posts pertaining to a given event over time, a task referred to as story detection. Moreover, there are often several different stories pertaining to a given event, which we refer to as sub-stories and the corresponding task of their automatic detection as sub-story detection. This paper proposes hierarchical Dirichlet processes (HDP), a probabilistic topic model, as an effective method for automatic sub-story detection. HDP can learn sub-topics associated with sub-stories which enables it to handle subtle variations in sub-stories. It is compared with state- of-the-art story detection approaches based on locality sensitive hashing and spectral clustering. We demonstrate the superior performance of HDP for sub-story detection on real world Twitter data sets using various evaluation measures. The ability of HDP to learn sub-topics helps it to recall the sub- stories with high precision. Another contribution of this paper is in demonstrating that the conversational structures within the Twitter stream can be used to improve sub-story detection performance significantly.