Our hypothesis is that drugs and diseases sharing similar biomedical and genomic concepts are likely to be related, and thus repositioning opportunities can be identified by ranking drugs based on the incidence of shared similar concepts with diseases and vice versa. To test this, we constructed a probabilistic topic model based on the Unified Medical Language System (UMLS) concepts that appear in the disease and drug related abstracts in MEDLINE. The resulting probabilistic topic associations were used to measure the similarity between disease and drugs. The success of the proposed model is evaluated using a set of repositioned drugs, and comparing a drug's ranking based on its similarity to the original and new indication. We then applied the model to rare disorders and compared them to all approved drugs to facilitate "systematically serendipitous" discovery of relationships between rare diseases and existing drugs, some of which could be potential repositioning candidates.