If you fail to draw the chosen number, the remaining number of cards fly from the deck on their own and take effect all at once.
If you declare three, and you only draw one, then after an hour the other two come out of the deck and take effect immediately. That doesn't completely solve the conundrum you've asked about, so the DM will need to make a ruling on which card takes effect first, but the description suggests that you aren't drawing the cards, they are being drawn for you. Let's call that "autodraw."
That avoids the 'draw no more cards' conundrum.
Example:
First card: Jester (yay, XP for you)
Fail to draw, one hour later ...
Second Card (autodraw): Donjon (you are trapped!)
Third Card (autodraw): The Fates (you can undo Donjon, lucky you)
or
Third Card: Balance (you are trapped and you change alignment).
or
Third Card: Knight (The DM may rule that he appears wherever you are trapped, so maybe he can help you get out).