The 64th question: Let $S=\left\{a_{1}, a_{2}, \ldots, a_{n}\right\}$ be a non-empty family of subsets $U$ with the property: if $A \in U, A \subseteq B$, then $B \in U$; and let $S$ be a non-empty family of subsets $V$ with the property: if $A \in V, A \supseteq B$, then $B \in V$. Find the maximum possible value of $\frac{|U \cap V|}{|U| \cdot|V|}$.