Summary. Competing risks are classically summarized by the cause-specific hazards and the cumulative incidence function. To obtain a full understanding of the competing risks, these identifiable quantities should be viewed simultaneously for all events. Another available quantity is the conditional probability of a competing risk, which is defined as the cumulative probability of having failed from a particular cause given that no other (competing) events have occurred. When one event is of a particular interest, this quantity provides useful insights, as it displays a probability adjusted on the other competing events. In certain applications, this interpretation may be preferable to that for the cumulative incidence function in quantifying cause-specific cumulative failure probabilities. The use of the conditional probability has been limited by the lack of a regression modelling strategy. We apply recently developed regression methodology to the conditional probability function and illustrate, by using a data set on patients suffering from monoclonal gammopathy of unknown significance, the insights that are gained from this methodology.