The terms "probiotics" and "prebiotics" aren't really food terms and don't apply very well to food. These terms come from the dietary supplements industry.
"Probiotics" usually refers to a dietary supplement that contains bacteria (usually freeze-dried) in amounts likely to remain viable in our digestive tract after we've swallowed the supplement. In order to guarantee that some of the freeze-dried bacteria become viable in our digestive tract, large numbers of bacteria are usually contained in a single capsule. For example, a one-gram capsule of Lactobaccilus bacteria might contain 250 billion colony-forming units (or cfu) of the bacteria.
"Prebiotics" usually refers to a dietary supplement that contains nutrients that serve as food for certain bacteria in our digestive tract. FOS, or fructo-oligosaccharides, is one example of a nutrient often contained in a "prebiotic" supplement. Inulin (a special storage form of partly indigestible starch found in many root vegetables foods including onion and garlic) is another commonly encapsulated "prebiotic."
If you compare the world of supplements to the world of food, you will find that "probiotics" and "prebiotics" are somewhat strange terms. The vast majority of the World's Healthiest Foods are not foods that we eat in order to obtain their bacteria. Although there are almost always bacteria present in any food that we eat, bacteria are seldom concentrated in the World's Healthiest Foods and it would not make sense to have any concentrated bacteria in them.
One exception to this rule would be cultured dairy foods. Cultured dairy foods such as yogurt and kefir can be great sources of "healthy" or "friendly" bacteria. In this case, the term "friendly" bacteria simply means bacteria that are needed for healthy digestion in our intestinal tract (and proper balancing of different bacterial populations). I would just be careful to read the labels and choose a high quality product that says it has live active cultures. Because dairy products are often cultured with these exact bacteria to make yogurt and kefir, they can be highly beneficial in this regard, provided that a person can tolerate them without any adverse reaction.
In most prepackaged, processed foods, however, it is unlikely to find any sizable quantities of live bacteria ("probiotics") due to the use of heat and chemicals in food processing. This same situation can take place with cultured dairy products, such that yogurts and kefirs can contain no live bacteria cultures even though live bacteria were at one time added to the milk. For this reason, it's important to select cultured dairy products that indicate "contains live cultures" or "contains active cultures" on the packaging. Some manufactures will actually report the amounts of live culture contained in the product.
Live bacterial cultures can be added to other foods besides dairy foods. Sauerkraut—another name for fermented cabbage—is an example of a cultured vegetable. An Asian version of fermented cabbage, particularly popular in Korea, is called kim chee. A basic fermentation process is used to culture the cabbage in kim chee, and chili pepper, garlic, and salt are typically added to give this cultured vegetable its pungent character. As with cultured yogurts and kefirs, these fermented vegetables may or may not contain active bacterial cultures. Once again, the manufacturers who are sensitive to these issues will often indicate the presence of live bacteria cultures (if they are present) on the packaging. Miso, a thick paste often made from soybeans, is another example of a cultured food that can contain live bacterial populations.
Remember how I explained earlier that FOS are nutrients often contained in prebiotic dietary supplements? Well, you can get these same FOS nutrients in foods as well. Since Jerusalem artichokes and chicory root both have concentrated amounts of FOS, these foods could be considered as "prebiotic" in the dietary supplement sense of that term. Earlier I also mentioned the popularity of prebiotic dietary supplements containing inulin, a storage carbohydrate (technically called a fructan). Inulin—and other inulin-type fructans—can also be found in many root vegetables, including onion, jicama root, dandelion root, burdock root, leeks, and asparagus.
Fibers found in many foods, including oats, barley, and apples can be fermented into short chain fatty acids that help to feed the beneficial bacteria in our intestines. For this reason, it is also possible to think about these foods as "prebiotic." In fact, I would tend to think about any high-fiber food that contained fairly digestion-resistant fibers or starches as "prebiotic," and you can find many such foods in my World's Healthiest Foods list. The digestion-resistant fibers and starches found in these foods can be metabolized inside our lower digestive tract and converted into butyrate, propionate, and other short-chain fatty acids that can be used by our intestinal bacteria for energy.
For more information on this topic, please see:
Annison G, Topping DL. Nutritional Role of Resistant Starch: Chemical Structure Vs Physiological Function. Annu Rev Nutr. 1994;14297-320.
Brown I. Complex Carbohydrates and Resistant Starch. Nutr Rev. 1996;54(11 Pt 2):S115-9.
Asp N. Resistant Starch--an Update on Its Physiological Effects. Adv Exp Med Biol. 1997;427:201-10.
Roberfroid MB. Prebiotics and probiotics: are they functional foods? American Journal of Clinical Nutrition. 2000;71(6): 1682-7S.
Topping DL, Clifton PM. Short-Chain Fatty Acids and Human Colonic Function: Roles of Resistant Starch and Nonstarch Polysaccharides. Physiol Rev. 2001;81(3):1031-64.