Dr. G has spent his last weekend with analyzing $n$ number of cards which are numbered from $1$ to $n$. He has a fair shuffling machine for his cards and while playing and drawing some cards, he uses his shuffling machine all the time.
After a while, he noticed something interesting. He usually encounters two consecutive numbered cards at least once while drawing the cards orderly or randomly without shuffling them back to the deck until he has no card in the deck.
First of all, he got shocked how come he encounters two consecutive numbered cards most of the time after shuffling them in a fair shuffling machine because there were many cards he was drawing and firstly the chance to see two consecutive cards in a row seemed very low to him. Then he noticed something and he put some numbers on a paper and come up with an interesting theorem.
Dr. G's Theorem: Even if there are infinite number of cards which are numbered sequentially from $1$ to $n$, where $n$ is a positive integer number, your chance to encounter two consecutive numbered cards at least once cannot be less than $x \%$ until you draw all the cards which are shuffled fairly.
Is this theorem true, if so, what is $x$?