I am trying to find the conditional probability distribution function of $Y$ $$F(Y\mid X_1,X_2)$$ given that $Y$ is distributed uniformly on $[0,1]$, $$X_1=Y+Z_1$$ and $$X_2=Y+Z_2$$ where $Z_1$ and $Z_2$ are also drawn independently from each other and from $Y$ according to the uniform distribution on $[0,1]$.
How does the result change if we have $X_1=m Y+nZ_1$ for some real $m,n$?
It seems to be an easy question, but I cannot come to any meaningful answer. Thank you for any hints.