Ring Pro Install Existing Wiring

Hello, I’m installing a Ring Video Doorbell Pro (Wired). Can someone help confirm if I can use the existing wiring? The chime is very old. It is also set up to ring two different chimes. There are two doors on the house. Each door rings the same chime, but with different chime sound. Attached is a picture. If I need a transformer I can pick one up. But will I be able to piggy back off the chime and still keep one of the doors on old bell with one door on Ring?