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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

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What is the probability that $X_i$ is the $k^{th}$ order statistic in consecutive trials?

Consider $n$ r.vs ${X_1, X_2,...,X_n}$. Each is i.i.d drawn from some distribution $f(.)$. What is the probability that $X_i$ is the $k^{th}$ order statistic in any two consecutive trials?
Suvadip Batabyal's user avatar