Probiotics are mostly to replenish the normal gut microflora.
Clearly this would be an issue for bacterial hemorrhagic colitis, but any situation where diarrhea is occurring could conceivably benefit as well. No, and that is why you have to rule out everything else before assigning this diagnosis. It may actually be several diseases, for all we know. Vomiting is not a typical symptom of lactose intolerance. There may have also been some other intolerance going on.