Let $X_1, X_2, \dotsc , X_n$ iid random sample of size $n$ from an exponential distribution with mean $1/λ$. and $S$ is sum of $X_i$. Find the joint conditional pdf of X1, X2, . . . , Xn given S

i think S~Gamma($n$, $λ$) and joint conditional pdf =$f(x_1,x_2,x_3,\dotsc x_n,S)/f_s(S)$

I think $f_s(S)$ is Gamma distribution's pdf but i can't calculate joint distribution pdf $f(x_1,x_2,x_3,\dotsc,x_n,S)$ because $S$ is sum of $X_i$. very confusing

How can solve this??

Let $X_1, X_2, \dotsc , X_n$ iid random sample of size $n$ from an exponential distribution with mean $1/λ$. and $S$ is sum of $X_i$. Find the joint conditional pdf of $X_1, X_2, \ldots , X_n$ given $S$

i think $S\sim\operatorname{Gamma}(n, λ)$ and joint conditional pdf $=f(x_1,x_2,x_3,\dotsc, x_n,S)/f_s(S)$

I think $f_s(S)$ is Gamma distribution's pdf but i can't calculate joint distribution pdf $f(x_1,x_2,x_3,\dotsc,x_n,S)$ because $S$ is sum of $X_i$. very confusing

How can solve this??