With the emergence and expansion of credit derivatives, which are financial instruments that are based on corporate bonds and provide their holders a protection against default, the importance of estimating probabilities of default has reached an unprecedented level. We have developed a Bayesian model to estimate term structures of conditional probabilities of corporate default, in an incomplete information setting. In such settings, investors do not have a complete picture of the economy nor of the true financial status of a firm. Therefore, we introduce a stochastic frailty to capture this unobservable source of uncertainty and to model default clustering. Frailty is found to have an impact on conditional default probabilities and on the default correlation between firms. The resulting values are well above those predicted by observable stochastic covariates: US interest rates, US Personal Income and a firm's distance-to-default.