Existing doorbell not working with ring doorbell 3 Help!!!

I have recently purchase ring doorbell 3.I have set it up and connected it over my existing doorbell with the relevant wires going to the relevant connectors on the back of the ring doorbell 3.I am having trouble with my existing doorbell. I understood that I could connect my existing doorbell to the ring doorbell 3.The existing doorbell I have I believe is mechanical. The existing bell makes a ‘ringing sound’ and the sound is dependent on how long you press it. I have attached some pictures of the doorbell and the transformer, hopefully this will give a better understanding of what we have.Could you please review and tell me if you can where I am going wrong on getting my existing doorbell to work with my ring doorbell 3.Thanks All