= Solution
For individual $i$, let $N_i(t)$ count its observed event by time $t$ and let $Y_i(t)$ indicate membership of the <risk set> immediately before $t$. Set $N=\sum_iN_i$ and $Y=\sum_iY_i$. Under a common <hazard function> $h(t)$ and <independent censoring>, a currently at-risk subject has event probability $h(t)dt+o(dt)$ in the next short interval. Summing over the current <risk set> gives the conditional intensity
$$
\mathbb E[dN(t)\mid\mathcal F_{t-}]=Y(t)h(t)dt=Y(t)dH(t).
$$
Equivalently, the event count decomposes as
$$
N(t)=\int_0^tY(u)dH(u)+M(t),
$$
where $M$ is the mean-zero <counting-process martingale> obtained by subtracting its conditional compensator. Estimating the unknown hazard increment by the observed event increment divided by the <risk set> size gives the <Nelson–Aalen estimator>
$$
\boxed{\widehat H(t)=\int_0^t\frac{\mathbf1_{\{Y(u)>0\}}}{Y(u)}\,dN(u)
=\sum_{a_j\leq t}\frac1{r_j}.}
$$
Here $a_j$ are the distinct observed event times and $r_j=Y(a_j)$ includes the subject who is about to fail. A censored observation affects subsequent <risk sets>, but causes no event jump. This is the requested no-ties estimator; tied event counts would produce $d_j/r_j$.
The derivation also identifies the estimation error:
$$
\widehat H(t)-\int_0^t\mathbf1_{\{Y(u)>0\}}\,dH(u)
=\int_0^t\frac{\mathbf1_{\{Y(u)>0\}}}{Y(u)}\,dM(u).
$$
Thus it estimates $H(t)$ on the time range where individuals remain at risk. It is not exactly unbiased for the entire cumulative hazard after the last risk set disappears. Its usual <Nelson–Aalen variance estimator> is $\sum_{a_j\leq t}r_j^{-2}$, since the compensator variance increment of the no-ties event process is $Y\,dH$.
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