The dropper may be placed in boiling water to sanitize if needed.  However, it is normally not needed to rinse, clean or sanitize the dropper.  The dropper should be replaced into the bottle after each use and sealed tightly.  Should it be necessary to clean and sanitize the dropper then it must be completely DRY before replacing in the bottle.  Water being introduced into the probiotic will cause the microencapsulation to fail and reduce the potency of the product.  Also water introduced into the oil will likely allow for undesirable mold and other microbial growth to occur rapidly.