Why did Ben Price suspect Jimmy of robbing banks?

When Jimmy is released from prison in the opening part of "A Retrieved Reformation," he goes to the rented room that has been kept for him by Mike Dolan to get his suitcase full of specialized safe-cracking tools. The reader learns that Jimmy had had a previous run-in with the bank detective Ben Price.

There on the floor was still Ben Price's collar-button that had been torn from that eminent detective's shirt-band when they had overpowered Jimmy to arrest him.

So Ben Price knows Jimmy to be a safe-cracker because he had already arrested him at least one time. This was for what the author describes as the "Springfield job" for which Jimmy was sentenced to four years in state prison but managed to get pardoned after serving only ten months.
Once Jimmy obtains his set of burglar tools he commits three bank jobs. Ben Price is called in to investigate because of the size of the loot and the rapid sequence of the robberies. He may not know Jimmy very well personally, but he knows a lot about him from his modus operandi and his reputation in the underworld. 

Ben Price investigated the scenes of the robberies, and was heard to remark: “That's Dandy Jim Valentine's autograph. He's resumed business. Look at that combination knob—jerked out as easy as pulling up a radish in wet weather. He's got the only clamps that can do it. And look how clean those tumblers were punched out! Jimmy never has to drill but one hole. Yes, I guess I want Mr. Valentine. He'll do his bit next time without any short-time or clemency foolishness.”

Jimmy is the best safe-cracker in the business. But his reputation is becoming a handicap because he is too conspicuous. For this reason he decides to move to an entirely new territory, to change his name, and to open a legitimate shoe business as a "front" behind which he can continue to operate as a safe-cracker. But he didn't reckon on falling in love at first sight with Annabel Adams. He decides to reform because he knows a girl like her could never love a criminal. Unfortunately, Jimmy's nemesis, Ben Price, is already on his trail because of those three bank jobs he committed after being released from prison.
Ben is prepared to arrest Jimmy, but by the sheerest coincidence he sees Jimmy make a noble sacrifice of his freedom, his fiancee, and his profitable business when he uses his burglar tools to save the life of a little girl who had accidentally gotten locked inside the bank vault.