Calculate conditional distribution

Question

Here are the processes of signal $s_i$ and $s_j$: \begin{equation} s_i = \theta+\sigma\varepsilon_i \end{equation} \begin{equation} s_j = \theta+\sigma\varepsilon_j \end{equation} where $\varepsilon_i$ and $\varepsilon_j$ are independent and normally distributed with mean $0$ and variance $1$. That is, $\varepsilon_i\sim N(0,1)$, $\varepsilon_j\sim N(0,1)$. $s_i$ and $s_j$ share the same $\theta$ and $\sigma$, where $\theta$ is independent to $\varepsilon_i$ and $\varepsilon_j$ and $\sigma$ is a positive constant. My question is, given condition $s_i$ and $\theta>k$, what is the conditional distribution of $s_j$? My solution is given by: \begin{equation} Prob(s_j\leq x|s_i, \theta>k)=Prob(s_j-s_i\leq x-s_i|s_i,s_i-\sigma \varepsilon_i>k)=Prob(\sigma (\varepsilon_j-\varepsilon_i)\leq x-s_i |s_i, \varepsilon_i<\frac{s_i-k}{\sigma}) \end{equation} But then I do not know how to move on... Can anyone teach me how to calculate this conditional distribution? Thanks!