A 2017 article from the United Kingdom on feeding commercially available probiotics to shelter dogs to prevent diarrhea:
Efficacy of a Probiotic-Prebiotic Supplement on Incidence of Diarrhea in a Dog Shelter: A Randomized, Double-Blind, Placebo-Controlled Trial - Rose - 2017 - Journal of Veterinary Internal Medicine - Wiley Online Library . Summary: The treatment was effective, and the product used is publicly available:
Dogs - Veterinary - Products - Protexin . Bad news: The product is not distributed in the US.