Here's a review article from 2016 that is favorable on the use of probiotics:
Understanding the canine intestinal microbiota and its modification by pro-, pre- and synbiotics – what is the evidence? - Schmitz - 2016 - Veterinary Medicine and Science - Wiley Online Library . However, this article is skeptical about the quality of currently available commercial products, citing the article about the 19 commercial dog foods that I linked to above:
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Quality control is also an issue with probiotic products. As they are usually classified as nutritional supplements, quality control as for drugs is not legally required. Again, no large amount of data are available on the quality, shelf-life, etc., of commercially available probiotics. One study has assessed microbial components of dog food claiming to contain probiotics (Weese & Arroyo
2003). None of the 19 commercial diets contained all the claimed organisms, whereas one or more of the listed components could be isolated from around 50% of samples. Eleven samples contained additional, related organisms and more than 25% of tested diets showed no relevant bacterial growth.
To the authors’ knowledge, no published study has so far assessed whether the claimed bacterial quality or quantity in probiotic nutritional supplements is according to label claims."