Did he have a food change to cause the diarrhea? I have found that the dog probiotics that you can buy in the syringe is the best. I can buy it in our local store, but I don't think you can get it everywhere. I first got it from my vet. If he hasn't had a vet check and he is new to you, I would take him to the vet, you don't want your other dogs infected with anything he could bring in. A stool and blood test could be very worthwhile. He isn't going to come around if he is ill.
Primal, minus eggs, dairy and a myriad of other allergens.