设随机变量 $X_i \sim\left(\begin{array}{ccc}-1 & 0 & 1 \\ \frac{1}{4} & \frac{1}{2} & \frac{1}{4}\end{array}\right)(i=1,2)$, 且满足 $P\left\{X_1 X_2=0\right\}=1$ ，则 $P\left\{X_1=X_2\right\}$ 等于
$\text{A.}$ 0
$\text{B.}$ $\frac{1}{4}$
$\text{C.}$ $\frac{1}{2}$
$\text{D.}$ 1