Kaplan-Meier Estimate

#1
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.