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In standard methodology for natural language processing, entities in text are typically embedded in dense vector spaces with pre-trained models. The embeddings produced this way are effective when fed into downstream models, but they require end-task fine-tuning and are fundamentally difficult to interpret. In this paper, we present an approach to creating entity representations that are human readable and achieve high performance on entity-related tasks out of the box. Our representations are vectors whose values correspond to posterior probabilities over fine-grained entity types, indicating the confidence of a typing model's decision that the entity belongs to the corresponding type. We obtain these representations using a fine-grained entity typing model, trained either on supervised ultra-fine entity typing data (Choi et al. 2018) or distantly-supervised examples from Wikipedia. On entity probing tasks involving recognizing entity identity, our embeddings used in parameter-free downstream models achieve competitive performance with ELMo- and BERT-based embeddings in trained models. We also show that it is possible to reduce the size of our type set in a learning-based way for particular domains. Finally, we show that these embeddings can be post-hoc modified through a small number of rules to incorporate domain knowledge and improve performance.