Past exam of the mathematics course of the University of Cambridge / 2015 / iii / Paper 35 / 7 / 4

Letting $t\to \infty$ in the cumulative incidence function gives the probability that the observed first event is of type A:This is the sense of occurrence in the competing risks model. If one instead followed the latent exponential $T_A$ even after B, its eventual-occurrence probability would be one; that is a different question from observing A before the competing event.