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

This is the first major site of host enzymatic digestion. A combination of low pH and enzyme activity may prevent some probiotics reaching the target region in the small and large intestine.

What solution could be provided by a probiotic?

Look for probiotics with resistant characteristics to withstand the acidic environment in the stomach. For example, spore formers (e.g. Bacillus spp), structurally stable heat inactivated Lactobacillus spp. or a robust, viable Lactobacillus spp that can reach the target region in the small and large intestine to benefit the animal.