## Kaplan-Meier Estimate

Let is the survival time for individual and be the time to censoring. Let . And is the Kaplan-Meier estimator for the censoring distribution. Suppose and are two indicator functions. Also, is a probability. Consider the following estimator of cumulative distribution function:

where is an indicator function.

Now it is written that, with no censoring becomes

I understand that if there is no censoring, then , that is, we will always observe the survival time. Also, with no censoring and hence .

But I do not understand why does Kaplan-Meier estimator for the censoring distribution, , which appears in the above first equation vanish in the second equation with no censoring?