Is there a non-constant distribution $\mathbb{D}$ such that if $X_1, ..., X_n \sim \mathbb{D}$ are iid random variables with order statistics $Y_{(1)}, ..., Y_{(n)}$, then the distribution of $Y_{(i)} | Y_{(1)}, ..., Y_{(i-1)}$ is identical?
The constant distribution (say $X_i=1$ w.p $1$) satisfies this. My intuition says no, but then again I'm not sure if it might be true for something like the exponential distribution (or similar families) because of the memorylessness property.