Kaplan–Meier telescoping across a censor-free interval ($\hat{S}(b)=\hat{S}(a)(r-d)/r$)

For a fixed cohort with $r$ individuals at risk just after $a$, no censoring or entry inside $(a,b)$, and $d$ events in $(a,b]$, the Kaplan–Meier estimator factors telescope to the displayed ratio. A tied group of $d_j$ events contributes $(r_j-d_j)/r_j$, the same product as any sequential ordering without intervening censoring. Events at $b$ are counted before censoring at the same time under the usual convention.