Bayesian predictive power is the expectation of the probability to meet the primary endpoint of a clinical trial, or any statistical test, at the final analysis. Expectation is computed with respect to a distribution over the true underlying effect and Bayesian predictive power is a way of quantifying the success probability for the trial sponsor while the trial is still running. The existing framework typically assumes that once the trial is not stopped at an interim analysis, Bayesian predictive power is updated with the resulting interim estimate. However, in blinded Phase III trials, typically an independent committee looks at the data and no effect estimate is revealed to the sponsor after passing the interim analysis. Instead, the sponsor only knows that the effect estimate was between predefined futility and efficacy boundaries. We show how Bayesian predictive power can be updated based on such knowledge only and illustrate potential pitfalls of the concept.