When a finesse is less than 50%

Suppose you are declarer in 6♠ on this deal from the IBPA:

                ♠ 7 4 2
                ♥ A Q 7 6 4 3
                ♦ ---
                ♣ 10 8 7 5
♠ J 10 9 3                   ♠ ---
♥ 9 8 2                      ♥ K J 10
♦ J 5 3 2                    ♦ K Q 10 9 8 4
♣ Q 3                        ♣ J 9 6 4
                ♠ A K Q 8 6 5
                ♥ 5
                ♦ A 7 6
                ♣ A K 2

West leads the ♠J and East show out and discards a diamond. One plan is to finesse the ♥Q, planning to discard a club loser if it wins. That line of play won't work, and you will be defeated.

A finesse is a 50% proposition, right? Not so fast. Once West is known to hold four spades and East one diamond, West had only nine places for the ♥K as compared to East's 12. Also, the plan involving the heart finesse relies on West's having at least two diamonds, reducing the chance of success to 32%.

A better plan is to try and establish a second heart trick by ruffing hearts in the South hand. This will work when the ♥K is tripleton or shorter and West has at least two diamonds.

The play goes like this: Win the spade lead, play a heart to the ace, and ruff a heart. Next ruff a low diamond and ruff another heart. Finally, ruff your other low diamond and discard a club on the good heart. West can ruff in, but South takes the rest.

The overall chance of success for this plan is a little more than 50%.