The Hunter and the Hunted (2004)

Jin (Yakusho), a young, widowed police detective who is thinking of leaving the force to better take care of his 8 year old daughter Misaki (Kanno), by chance arrests Neko (Emoto), an accomplished middle aged burglar who has just fixed Misaki's bicycle. After Neko has several weeks to see Jin in the interrogation room, he decides to confess to Jin and teach him how to become a capable detective and worthy adversary. By the time Neko serves his 10 year sentence, Jin is a highly regarded detective and they can they start their contest in earnest.