Let T_i is the survival time for individual i (i=1,2,\ldots, n) and C_i be the time to censoring. Let U_i=\min(T_i,C_i). And \hat S(U_i) is the Kaplan-Meier estimator for the censoring distribution. Suppose R_i and Z_i are two indicator functions. Also,p is a probability. Consider the following estimator of cumulative distribution function:

\hat F(t)= \sum_{i=1}^{n}\frac{I(T_i<C_i)(1-R_i+R_iZ_i/p)I(U_i\le t)}{\hat S(U_i)},
where I(.) is an indicator function.

Now it is written that, with no censoring \hat F(t) becomes

\hat F(t)= \sum_{i=1}^{n}(1-R_i+R_iZ_i/p)I(T_i\le t).

I understand that if there is no censoring, then I(T_i<C_i)=1, that is, we will always observe the survival time. Also, with no censoring U_i=T_i and hence I(U_i\le t)=I(T_i\le t).

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

Thanks in advance.