Choose a number X from {1,2,3,4,5}. Now choose a number from the subset {1.....X}. Call this second number Y.
P{X|Y=1} = 1/5
P{X|Y=2| = 1/4
P{X|Y=3} = 1/3
P{X|Y=4} = 1/2
P{X|Y=5} = 1
Are these probabilities correct? These event are not independent?