1. A method comprising: generating a noisy result using a differentially private computation from a private data set by a computing device, wherein the differentially private computation adds noise to the private data set using an exponential mechanism; determining a conditional distribution of the differentially private computation wherein the conditional distribution describes a probability distribution for the noisy result; determining a posterior distribution for the differentially private computation by the computing device using preexisting knowledge about one or more records of the private data set and the conditional distribution, wherein the preexisting knowledge comprises one or more of information about a user whose data is part of the private data set or information about a total number of records of the private data set; wherein determining the posterior distribution using the preexisting knowledge about the one or more records of the private data set and the conditional distribution comprises: retrieving a plurality of results from previous executions of the differentially private computation that were generated in response to previously received queries; and inferring the posterior distribution using the conditional distribution, the plurality of results, and the preexisting knowledge about the one or more records of the private data set using probabilistic inference; and providing the posterior distribution by the computing device, wherein the posterior distribution includes the probability that the generated noisy result is a true result from the private data set.