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.