  Let $n, u \geq 0$, $M$ be a ($n$+$u$) $\times$ $n$ matrices over
$\mathbb{Z}_p$, and $G$ be a finite abelian p-group group. We find that the
probability that the cokernel of $M$ is isomorphic to $\mathbb{Z}_p^u \oplus G$
as $n$ goes to infinity is exactly what is expected from Cohen-Lenstra
heuristics for the classical case when $u$ is negative.
