Suppose that $x_1$, $x_2$ and $x_3$ are three random variables such that
$$x_1=a+e,$$ $$x_2=a+u$$ and $$x_3=a+t$$
where $a\sim N(\mu_a,\sigma_a^2)$, $e\sim N(0,\sigma_e^2)$, $u\sim N(0,\sigma_u^2)$ and $t\sim N(0,\sigma_t^2)$. Moreover, $a$ ,$e$ , $u$ and $t$ are independently distributed. We define the set $I=\{x_1, x_2, x_3\}$
How can we compute the following
$$\mathbb{E}\left[a^2|I\right]$$