Structure of discrete order statistics (Q1071420)

X\({}_ 1,...,X_ n\) are independent and identically distributed discrete random variables, the common distribution having at least three points in its support. \(Y_ 1\leq Y_ 2\leq...\leq Y_ n\) denote the ordered values of \(X_ 1,X_ 2,...,X_ n\). Define the event \(A_{k,m}\) as \(\{Y_ k=a_ k,Y_{k+1}=a_{k+1},...,Y_ m=a_ m\}\) for \(1\leq k\leq m\leq n.\) A formula for \(P(A_{i+1,j}| A_{h,i})\) for \(1\leq h\leq i<j\leq n\) is developed and discussed.