The short story makes it clear that Mary Maloney is no stranger to the detectives who come to her home and investigate the death of her husband. Because her husband was a policeman himself, it is clear that she would have known some of the fellow men that she worked with in the force, and that those same men who came to investigate his somewhat suspicious murder would be ones that she knew through her husband. This is supported by the following quotation from the text:
She know them both--she know nearly all the men at that precinct--and she fell right into a chair, then went over to join the other one, who was called O'Malley, kneeling by the body.
The quote clearly states how she knew "nearly all the men" in that police precinct, and this is later supported when the narrator informs the reader that she knew one of the detectives who arrived slightly later on. This is something that Mary is fully aware of, and she hopes that their knowledge of her as a wife who was absolutely "devoted" to her husband will play into her hands. What is so ironic in this short story is the way that a character who starts off at the beginning of the story as being nothing more than a loving housewife shows herself to be something of a criminal genius. She clearly uses her familiarity with the policemen who arrive to her advantage, encouraging them to eat the murder weapon and therefore creating the perfect murder.