Modern search engines increasingly incorporate tabular content, which consists of a set of entities each augmented with a small set of facts. The facts can be obtained from multiple sources: an entity's knowledge base entry, the infobox on its Wikipedia page, or its row within a WebTable. Crucially, the informativeness of a fact depends not only on the entity but also the specific context(e.g., the query).To the best of our knowledge, this paper is the first to study the problem of contextual fact ranking: given some entities and a context (i.e., succinct natural language description), identify the most informative facts for the entities collectively within the context.We propose to contextually rank the facts by exploiting deep learning techniques. In particular, we develop pointwise and pair-wise ranking models, using textual and statistical information for the given entities and context derived from their sources. We enhance the models by incorporating entity type information from an IsA (hypernym) database. We demonstrate that our approaches achieve better performance than state-of-the-art baselines in terms of MAP, NDCG, and recall. We further conduct user studies for two specific applications of contextual fact ranking-table synthesis and table compression-and show that our models can identify more informative facts than the baselines.