Probability of a 7

Basically, it doesn't matter that one of the cards is randomly on the floor when you draw yours. Even if $\frac{51}{52}$ of the cards randomly fell to the floor, your chance of drawing/taking that last card and having it be a 7 would still be $\frac{4}{52}$ -- 4 7's out of 52 cards.

If you're still not convinced, work it out with conditional probability. Since the card that falls out of the deck is random, there's a $\frac{4}{52}$ chance that the card that falls loose is a 7. If it was a 7, then you now have only a $\frac{3}{51}$ chance of drawing a 7 -- so there's a $\frac{3 \times 4}{51 \times 52}$ chance that you draw a 7 this way. But $\frac{48}{52}$ of the time, it wasn't a 7 that fell out, and that means you now have a $\frac{4}{51}$ chance of drawing a 7 -- so there's a $\frac{48 \times 4}{52 \times 51}$ chance that you draw a 7 this way.

$\frac{3 \times 4}{52 \times 51} + \frac{48 \times 4}{52 \times 51} = \frac{(3+48) \times 4}{52 \times 51}= \frac{51 \times 4}{52 \times 51} = \frac{4}{52}$