This is a follow up of What does it mean for a Poisson point process $\Phi$'s points in $A$, conditioned on $\Phi(A)=k$ to be uniform?
My question: Are there similar results for the more general renewal process?
To be specific, let's assume arrival time $T$ is sampled from a distribution $p(\cdot)$ on $(0,\infty)$, let $N_t$ be the number of arrivals between $0$ and $t$. What is the distribution of $( (T_1,T_2,...,T_n )| N_t = n)$?
