I wouldn't give it as a probiotic. I read an article that the human probiotics in yoghurt don't work on a hamster! You can buy probiotics for hamsters though. Some people use Pro C, Cypher on here uses the one linked below. Bene bac is good too - that is mainly sold in the US - I managed to get it in the Uk. I liked it because it's just probiotics and no additives and vet recommended. Yes you can give it at the same time, but best to give it at a different time of day (eg mixed in a bit of baby food or porridge if it's a powder). I waited till I was near the end of the course and started the probiotic a couple of days before the end, then used it for two weeks.
https://ratrations.co.uk/potent-brew...arch=Probiotic
Bene bac plus (make sure it's the version for small animals)
https://www.amazon.co.uk/Bene-Bac-Sm...gateway&sr=8-8