Let $U_1, U_2, U_3 \sim \text{Uniform}(0, 1)$ be i.i.d. random variables. Let $U_{(1)} < U_{(2)} < U_{(3)}$ be their order statistics. What is the probability that $U_{(2)} > \frac{1}{2}$ given that $U_{(1)} < \frac{1}{4}$?