First off Mary was pregnant, which makes her an unlikely and sympathetic individual in such a condition. Second, the police officers all knew her as a very sweet and familiar person because her husband worked on the force. Third, after the murder, she had convinced herself so perfectly about her story that even she believed it:
That’s the way, she told herself. Do everything right and natural. Keep things absolutely natural and there’ll be no need for any acting at all.
Therefore, when she entered the kitchen by the back door, she was humming a little tune to herself and smiling.
“Patrick!” she called. “How are you, darling?”She put the parcel down on the table and went through into the living room; and when she saw him lying there on the floor with his legs doubled up and one arm twisted back underneath his body, it really was rather a shock. All the old love and longing for him welled up inside her, and she ran over to him, knelt down beside him, and began to cry her heart out. It was easy. No acting was necessary.
Fourth, she had an airtight alibi because of her verifiable trip to the grocer. Fifth, she got the officers to feel sorry for her; they even got her whiskey in order to keep her calm. And last, she got the officers to eat the murder weapon. Indeed, as Officer Noonan said:
It’s the old story,” he said. “Get the weapon, and you’ve got the man.”
No murder weapon, no man... or woman.
The detectives all knew Mary and knew her to be a loving, devoted wife--which she actually was up to the time her husband Patrick announced that he was leaving her. There are strong indications in the text that there had never been any hint of marital discord. Patrick was the kind of man who kept everything to himself. When he tells Mary he wants a divorce he takes her completely by surprise. He also shows that he has kept his dissatisfaction a strict secret.
"So there it is," he added. "And I know it's kind of a bad time to be telling you, but there simply wasn't any other way. Of course I'll give you money and see you're looked after. But there needn't really be any fuss. I hope not anyway. It wouldn't be very good for my job."
Patrick keeps regular hours. There is no suggestion that he is involved with another woman. Extramarital affairs are a common reason for spousal murders.
When the clock said ten minutes to five, she began to listen, and a few moments later, punctually as always, she heard the tires on the gravel outside, and the car door slamming, the footsteps passing the window, the key turning in the lock.
The fact that Mary is six-months pregnant is also in her favor. She would be unlikely to kill the man on whom she and her baby would be dependent for support. Her pregnant condition would also make it seem too difficult to commit such a violent murder. Mary must have been able to exert herself so strenuously only because she was suddenly charged with rage.
An implicit theme in "Lamb to the Slaughter" is that outsiders really can't tell much about what goes on in other people's marriages. Marriage is a very complicated relationship. Roald Dahl has this same implicit theme in a similar story: "The Way Up to Heaven."
Because Mary loved her husband and showed it to his co-workers, then went to the store owned by Sam to make sure that they would be convinced.