Probiotics work best and should be taken on an empty stomach before you have your meal.
So you could take the probiotics in the morning while you have an empty stomach and then by the time you have breakfast the probiotics should have enough time to work in your body properly.
You can take probiotics on a full stomach but it's always best to consume or take your probiotics while you have an empty stomach.
You'll get better results from the probiotics when the probiotics are taken on an empty stomach.
When you take probiotics you should also take adequate amounts of prebiotic fiber which helps the probiotics have a better environment in your stomach.