Let $ABC$ be a triangle with area $K$. Points $A^*$, $B^*$, and $C^*$ are chosen on $AB$, $BC$, and $CA$ respectively such that $\triangle{A^*B^*C^*}$ has area $J$. Suppose that \[\frac{AA^*}{AB}=\frac{BB^*}{BC}=\frac{CC^*}{CA}=\frac{J}{K}=x\] for some $0<x<1$. What is $x$?

[i]2019 CCA Math Bonanza Lightning Round #4.3[/i]