Given positive integers $n,d,\ell\ge1$ such that $n\ge 1+(d-1)\ell$, I must find a a function
$$
a=a(n,d,\ell),
$$
such that
\begin{align\*}
0< a(n,d,\ell)&<1,\\
\frac{n}{n-(d-1)(\ell-1)}a(n-1,d-1,\ell)&\le a(n,d,\ell),
\end{align\*}
for all $n,d,\ell\ge1,\ n\ge1+(d-1)\ell.$

I've been able to solve only the case $\ell=1$. In such a case, the function
$$
a(n,d,1)=\frac{n-d}{n-d+1}
$$
satisfy the requests.

Any help is appreciated.