Recently, Pitman\'s measure of closeness as a criteria of comparison of estimators and predictors faced considerable attention. In this paper, we discuss the asymptotic behavior of closeness probability in two samples of ordered data. We would consider the probability of closeness of two upper records to order statistic of future sample. First, using Bahadur representation of percentiles, it will be shown that the nearness probability of two predictors of Xk:n tend to the Pitman closeness probability of estimators of the pth population quantile, p when n increases. Then, we considered the exponential distribution and indicated the convergence with utilizing stirlings\' approximation.

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