[aces961]

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Let me make a simpler analougy for this.

I get N people, give them all a number between 1 and N randomly, as in put the numbers 1 to N in a big hat and let them draw from it.

This will give each person a random number between 1 and N, and it will be ordered as you put it.

Suppose I chose N randomly to begin with.

If a person drew the number 3 from the hat, there is a 50% chance that N<6.

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This last line is not necessarily correct unless you know the probality that N equals any given number. Thus in your original problem you are assuming the distribution of N to be something specific already, so any conclusions you make are based on themselves.