Let $X_i \stackrel{\mathcal L}{=} i \times U_i$ where $U_i$ are iid uniform $[0,1]$ time stamps $\sum$. (I don't quite get what time stamps means here, but I guess it means $U_i$ are uniformly distributed on $[0,1]$
The question is, for a certain $i$, would it be possible to calculate this probability:
$ \Pr \{\cap_{j < i} (X_j < X_i) \} $
In other words, what's the probability that $X_i$ is greater than any $X_j, j \in [1, i -1]$.