I am working on a slightly complicated conditional expectation operation. I have $v\sim U[a,b]$, $s_1=v+b_1$ and $s_2=v+b_2$, where $b_1,b_2\sim U[c,d]$ and finally $t=s_2+b_3$ where $b_3\sim U[e,f]$. I want to find out $E[v|s_1,t,s_2\geq h]$ where $h$ is a constant.
I know I have to deal with conditional density first. But given my conditions are in fact three of them, I don't know how to figure this out.