Inside the Magic Library at the Conjuring Arts Research Center

I'm going to be coy here: that's a classic in magic, with many possible solutions!

Not a magician, just a background in cognitive psychology. One way of manipulating these probabilities is by presenting specific cards ever so slightly longer while "ruffling" (not sure if this is the proper word, where you sequentially show each card in one smooth motion) the cards. You can do this for multiple cards and lower the amount of cards someone could've possibly chosen.

Another is by memorizing the order in which the cards were shown, and looking at subtle cues of arousal (mostly pupil dilation) indicating that a card has been picked...

Third, people don't uniformly randomly select cards, they have biases towards specific spots ( you wouldnt pick the absolute first card, nor the last one.. etc.)

Fourth, your deck doesn't ne essarily have 52 unique cards.. it just needs to seem like it while showing the cards.

It's a game of probabilities, but you can massage the probabilities in your favour. The shuffling at the end is just indirection..

Well, you already know that the technique used is called a "force". There's a book that collects 202 versions; probably it's in there somewhere.

I'll also be coy, but will make an observation: you described what you saw. but, you didn't describe everything that actually happened.