It is fine to give probiotics to dogs. Next time you are going to have to give Antibiotics , you should give your dog prebiotics beforehand. It really helps the system handle the Antibiotics . I had a dog with several autoimmune disorders, so I kept a bottle of prebiotics on hand.
You say that your dog is a finicky eater. Will he eat yogurt at all? I used to give one of my dogs yogurt mixed with pumpkin sometimes. She loved pumpkin. A lot of dogs will not like the texture of plain yogurt. Do you feed only dry food, or do you give wet food or raw food? Do you think you would be able to mix in a little bit of the contents of a capsule? I personally give human probiotics to my dog. You can give less because they don't have all of the added ingredients that seem to be in pet products. I would definitely recommend the probiotics as soon as he is finished with the Antibiotics .