How do you handle Rapscallion's Lucky Devil ability?

Lucky Devil let's you draw a card, if you draw the right card you regain Devil's Luck, if you draw a Joker wild things might happen. So far all is understood.

But what I'm wondering is:

After drawing a card and resolving its effect, do you put it back into the deck and reshuffle the whole deck? That way every draw would have the same odds.

Or do you put the card you just drew on a discard pile, thus the odds for your next draw change with every card drawn?

Or have you come up with a completely different procedure?