Label distribution can provide richer information about label polysemy than logical labels in multi-label learning. There are currently two strategies including LDL (label distribution learning) and LE (label enhancement) to predict label distributions. LDL requires experts to annotate instances with label distributions and learn a predictive mapping on such a training set. LE requires experts to annotate instances with logical labels and generates label distributions from them. However, LDL requires costly annotation, and the performance of the LE is unstable. In this paper, we study the problem of predicting label distribution from multi-label ranking which is a compromise w.r.t. annotation cost but has good guarantees for performance. On the one hand, we theoretically investigate the relation between multi-label ranking and label distribution. We define the notion of EAE (expected approximation error) to quantify the quality of an annotation, give the bounds of EAE for multi-label ranking, and derive the optimal range of label distribution corresponding to a particular multi-label ranking. On the other hand, we propose a framework of label distribution predicting from multi-label ranking via conditional Dirichlet mixtures. This framework integrates the processes of recovering and learning label distributions end-to-end and allows us to easily encode our knowledge about current tasks by a scoring function. Finally, we implement extensive experiments to validate our proposal.