You are playing this hand at 3NT having arrived there after you bid 1NT and North 3NT, East and West having passed throughout. Only you are vulnerable. (The hand is linked for reference; but you'd only actually get to see your hand and dummy as below, plus individual cards as they are played). Dummy is North, the lead (by West) is the 5 of hearts 6, T, won by J in hand.
AK9 63 AT94 J985 QT8 KJ7 QJ82 AK3
You have two chances for your ninth trick; a diamond finesse is 50-50. You also have an extra chance (8% by my calculation) if East has Qx of clubs, since you can drop the Q, then finesse against Tx remaining in West.
Since clubs is a "key" suit, I begin by inventorying the opponents' combined holding: QT7642. I start by playing the A, and expect the two lowest cards, 4 and 2 to drop (which in fact is the case). Say one opponent drops the 6 instead; I would then expect his partner to have the 4.
I lead the K, and sure enough, East drops the Q. But here's the tricky part; West drops the 7, meaning that the 6 and T are outstanding. Put another way, they can't both be playing their lowest card and at least one of them must be falsecarding!
Should I now suspect "chicanery," and go back to my 50-50 diamond finesse because my a priori 8% chance of a successful drop is now too low? (The actual South player tried a finesse which lost to East's ten.)
But perhaps South could now capitalize on the 3-3 break (36% a priori) by putting up his Jack, since the queen has been sacrificed. I can understand why East falsecarded, but why would West do so? Because if he hadn't I would have taken the club finesse, thinking that West had four cards and the queen was an honest drop from East. But faced with evidence of chicanery, I would suspect that E-W were trying to hide the fact that the diamond finesse would work.