  Given a random real quadratic field from $\{ \mathbb{Q}(\sqrt{p}\,) ~|~ p
\text{ primes} \}$, the conjectural probability $\mathbb{P}(h=q)$ that it has
class number $q$ is given for all positive odd integers $q$. Some related
conjectures of the Cohen-Lenstra heuristic are given here as corollaries. These
results suggest that the set of real quadratic number fields may have some
natural hierarchical structures.
