Alice draws a card from a standard deck, doesn't look at it, and gives it to Bob and he looks at it and says "it's not a King" (a spoiler of this type will, henceforth, be referred to as a Bob-Spoiler). Alice wants the probability that she'll draw a Queen next:
There are 51 cards left and 4 cards left for Alice to draw (3 if it has been drawn already). On average, it has not been drawn 11 out of 12 times (13 ranks, but we know that we can disregard the King from Bob's spoiler). Therefore I claim that the exact probability is:
$\frac{4*\frac{11}{12}}{51}$
And if Alice continues after n rounds (she lost $n-1$ guesses so far), we have:
$\frac{4*\frac{13-n}{13-n+1}}{52-n+1}$
(Please let me know if you disagree that this is the exact probability.)
My real intention of asking this question is me wanting an approximate and simple expression for the probability (which doesn't lose much accuracy even if Alice guesses after, say, a dozen cards have already been drawn (Bob-Spoilers have been dispensed every time). He varies this rank in his spoilers every time (distinct) so the maximum this little game can be played is with 13 drawn cards.)