What are the challenges in this part of the digestive tract?

A combination of low pH and host enzyme activity begins feed digestion but the bacteriocidal activity can prevent probiotics reaching the target region of the small intestine.

What solution could be provided by a probiotic?

Look for a probiotic that is administered in spore form. This will allow the organism to survive these chemical challenges that would destroy vegetative cells and allow it to reach the small intestine intact.