J.S.
Yes your breast milk will have some but it will be diluted. I have been giving my LO (4.5 months old) a 1/16th of a teaspoon of the infant powder probiotics twice a day once a week since she was 3 months. I do this because anymore than that seems to upset her stomach and as with most things it might be different for each baby. I tried giving her the recommended 1/4 teaspoon but it was just too much for her little system.
As she gets bigger I will probably start adding another day of the same dosage.