Sarah S. Comstock, PhD, is an Assistant Professor in the Department of Food Science & Human Nutrition at Michigan State University.
First, let's define probiotic: The precise definition of probiotics is the subject of ongoing discussions. For the purposes of the guidelines, probiotics are defined in accordance with the Food and Agriculture Organization of the United Nations (FAO) and World Health Organization (WHO) definition: “live microorganisms which when administered in adequate amounts confer a health benefit on the host.”
The short answer, is, yes, some probiotic bacteria are still alive when they reach the small intestine and even the large intestine, but they don’t populate those environments. Probiotic bacteria can only transiently populate the intestine. This means that if you stop taking the probiotic, you will no longer have that bacteria in your intestines.
For more information, check out "Are Probiotics Useful for the Average Consumer?" and "Fate, activity, and impact of ingested bacteria within the human gut microbiota."
Reference: Joint FAO/WHO Expert Consultation on Evaluation of Health and Nutritional Properties of Probiotics in Food including Powder Milk with Live Lactic Acid Bacteria. (2001). Health and nutritional properties of probiotics in food including powder milk with live lactic acid bacteria.