Until dynamical tropical cyclone ensemble prediction systems are more fully developed, quantification of the uncertainty in operational tropical cyclone intensity forecasts must be based on the record of past operational forecasts and the corresponding observations. Here, the recent Atlantic basin record is used to estimate a joint probability distribution of forecasts and observations, from which conditional probability distributions of the observation given a forecast value are derived. Qualitatively, if these conditional distributions are sharper than the unconditional distribution of intensity (climatological distribution), then knowledge of the forecast serves to reduce uncertainty about the observation, relative to knowledge of the climatological distribution alone. This average reduction in uncertainty due to knowledge of the forecast is quantified via calculation of the mutual information between the forecasts and observations, a concept borrowed from information theory. Mutual information, in this context, measures the average amount of information a forecast contains about the observation, which is equivalent to the average reduction in uncertainty about the observation due to knowledge of the forecast. Results show that for operational tropical cyclone intensity forecasts (NHC, GFDL, decay-SHIPS, SHIFOR), mutual information with the observations is positive for all lead times (0 to 5 days), meaning that even the longer lead forecasts reduce uncertainty relative to that of climatology. Comparing the mutual information for the various forecast systems elicits the possibility of using mutual information as a summary verification measure for tropical cyclone intensity forecasts. It is argued that mutual information merits serious consideration as a companion to mean absolute error, in particular because it can seamlessly include non-ordinal forecasts (e.g. "dissipated") with ordinal forecasts in the verification process.