In the superset label learning problem (SLL), each training instance provides a set of candidate labels of which one is the true label of the instance. As in ordinary regression, the candidate label set is a noisy version of the true label. In this work, we solve the problem by maximizing the likelihood of the candidate label sets of training instances. We propose a probabilistic model, the Logistic Stick-Breaking Conditional Multinomial Model (LSB-CMM), to do the job. The LSB-CMM is derived from the logistic stick-breaking process. It first maps data points to mixture components and then assigns to each mixture component a label drawn from a component-specific multinomial distribution. The mixture components can capture underlying structure in the data, which is very useful when the model is weakly supervised. This advantage comes at little cost, since the model introduces few additional parameters. Experimental tests on several real-world problems with superset labels show results that are competitive or superior to the state of the art. The discovered underlying structures also provide improved explanations of the classification predictions.