Police said the chance encounter was lucky because more than a week had passed since a woman reported her credit card stolen April 12, the Traverse City Record-Eagle reported Saturday.
Detective Kevin Gay pulled the purchase record for the credit card after it was reported stolen and determined the suspect had used it at two gas stations. He was able to pull surveillance footage of the male suspect from the first gas station and had taken an image of the man to the second gas station Thursday.
That was when he ran into the 51-year-old suspect buying a pack of cigarettes.
"The odds are definitely against this happening ... on the exact day and time he's in there, the suspect is in there buying a pack of cigarettes," said Capt. Brian Heffner.
Gay arrested the suspect, who is expected to face charges of unlawful use of a credit card, the newspaper said.