In recent years, there has been growing interest in reasoning with uncertainty in logic programming and deductive databases. However, most frameworks proposed thus far are either non-probabilistic in nature or based on subjective probabilities. In this paper, we address the problem of incorporating empirical probabilities -- that is, probabilities obtained from statistical findings -- in deductive databases. To this end, we develop a formal model-theoretic basis for such databases. We also present a sound and complete algorithm for checking the consistency of such databases. Moreover, we develop consistency-preserving ways to optimize the algorithm for practical usage. Finally, we show how query answering for empirical deductive databases can be carried out.