There's one quibble about this that might actually alter the answer for OP. Your numbers are correct for purely random shuffles, but a shuffle isn't purely random. A significant number of shuffles begin with a fresh deck where the cards are arranged in order and by suit. And a significant number of shufflers use the same methods, specifically the riffle, the overhand, or some other variant of those.

This is relevant to the field of cryptography, because humans are bad at simulating randomness. If you were to draw the top card from a shuffled deck, you probably have a lower chance of drawing an ace of spades than any other card, simply because the shuffler would not feel like they had shuffled if it was still on top. When picking lotto numbers, people tend to spread out their picks to get a quasi-even distribution across the available numbers, but it's just as likely to come up 1, 2, 3, 4, 5, and 6 as any other combination of numbers. Likewise, people playing with cards tend to cluster suits or pairs together when playing, so you'd be more likely to see those cards in proximity depending on the type of shuffle. Overhand tends to keep clumps together, and riffle or weave tend to interlace the cards in a way that still keeps pairs, sets, and runs close.

Of course, the difference would only be mathematically interesting, since in practice a good few shuffles is certainly close enough to completely random, especially if you start with a previously-shuffled deck. If you were trying to predict a card, your odds on any given draw is still going to be roughly 1 in 52.