By Andrew Robson 
Courtesy of AndrewBobson.co.uk
Here is the key extract from Sir Arthur Conan Doyle’s famous short story:
Gregory (Scotland Yard detective): “Is there any other point to which you would wish to draw my attention?”
Holmes: “To the curious incident of the dog in the night-time.”
Gregory: “The dog did nothing in the night-time.”
Holmes: “That was the curious incident.”
Many , many inferences at the bridge table are predicated on inaction. The negative inference. “If West had ‘A’, he would have done ‘B’. He did not do ‘B’, therefore he does not have ‘A'”.
Often the most revealing auction starts, “Pass, Pass,Pass”. You now know neither opponent has opening values.
In this example, you reach 4 ♥ having opened in the fourth chair after three passes. West leads out ♣ AKQ and you ruff the third round.
West would have opened the bidding if he held ♥ A in addition to ♣ AKQ. East has ♥ A and your only chance of avoiding a second trump loser is for him to have a doubleton. You cross to ♠ A and lead ♥ 2 towards ♥ K, East playing (say) ♥ 10. You return ♥ 5 and duck in dummy . If it’s your lucky day, East’s ♥ A will “beat air” and you can win his return , cash ♥ Q and drawing West’s (say) ♥ J and claim.
Note that if you knew West held ♥ A, you would lead to ♥ Q and duck on the way back.
West led ♠ J , East winning ♠ Q and cashing ♠ AK. At trick four he switched to ♦ 8. As declarer, you must try to avoid losing a trick to ♥ K and the a priori odds massively favour taking a finesse – crossing to dummy and running ♥ J, hoping for East to hold ♥ K, initially a 50-50 chance.
Not any more. East could not open the bidding , yet has AKQ: no room for ♥ K. Your only chance is that his ♥ K is singleton. You win ♦ 8 and cash ♥ A, telling West to hold back his cards (only kidding). Your luck is in – you had no idea his ♥ K was singleton. 4 ♥ made.