How do Mary’s words convince the policemen she is innocent?
Mary Maloney is able to convince the policemen by more than only her words. The author doesn't have Mary say that much to the policemen. She is able to be so convincing because of how she acts. She acts appropriately devastated and shocked at the fact that her husband is dead.
She fell into Jack Noonan's arms, crying uncontrollably. He put her gently into a chair.
"Is he dead?" she cried.
"I'm afraid he is. What happened?"
Mary has an alibi in place, and there is no evidence of a murder weapon. The other reason that the police officers do not suspect Mary is that she is well known to the officers. Mary's husband is a cop, so the officers know how much Mary adores Patrick.
The car came very quickly, and when she opened the front door, two policemen walked in. She knew them both. She knew nearly all the men at the police station.
No murder weapon, her alibi, her "devastation," and her immediately assumed innocence based on her being a friend all help to fully persuade each officer that she is not even close to being a suspect.
"It's not allowed by police rules, but since you're a friend."