What Are the Chances?

I was on my way to heating up my dumplings for lunch today when I realized that someone had shut the door to the kitchen in Mulholland Lounge, in spite of the large sign that says "DO NOT CLOSE DOOR TO KITCHEN."  There is a code lock on the door with the numbers 1 through 5 on it, and out of sheer luck, I happened to punch in 1-3-5, and the door opened.

Had I known that the combination was three numbers long, there would have been a 1/125 chance that I correctly guessed the sequence on my first try.  But what are the chances that the lock required three numbers AND that the three numbers were the ones I guessed on my first try?  The answer to that question requires a mathematical model that I am not willing or able to create.