Why did Valentine keep and hide his burglar's tools while he was in prison?

The simple answer is because he knew he would need them again. Jimmy Valentine, the expert safe-cracker, has just been released early from prison. The warden hopes that this will encourage him to give up his former life of crime and become a respectable, law-abiding citizen. However, as soon as he's released, Jimmy makes a beeline straight for the room over the restaurant where he was staying when the police arrested him. It's also the place where he hid the tools of his trade, the tools he used to crack safes. It's painfully obvious that the warden's hopes were misplaced; Jimmy never had any intention of keeping on the straight and narrow; he was always going to return to his former life of crime.
Once he's reunited with his tools, Jimmy embarks on a major crime spree, racking up a succession of thefts that leaves local law enforcement authorities reeling. But later on in the story, Jimmy's bag of tools will come in handy for a much more honorable purpose. On this occasion, Jimmy will use his tools, not for criminal gain, but to save a child's life.