Triangle $ABC$ is a right triangle with $\angle ACB=90^{\circ }$, $m\angle ABC=60^{\circ }$, and $AB=8$. Let $P$ be randomly chosen inside $△ABC$, and extend $\overline{BP}$ to meet $\overline{AC}$ at $D$. What is the probability that $BD<\frac{8\sqrt{3}}{3}$?