In Europe, if you need a room for 3 people you must reserve it as such, for two reasons. First, the fire laws are strict, so hotels are not willing to put more people in a room than it is rated for. Second, hotel rooms in general are much smaller than in the US, so you really need a room big enough for 3 people.
While triples are rarer than doubles or singles, they certainly exist. Some will be doubles with an extra bed shoe-horned in, and will be cramped, but others will be larger rooms that can hold three beds very comfortably (of course, the larger rooms will be pricier). The price differential between doubles and triples varies all over the map, due to these factors (many European hotels are in older buildings and have undergone multiple renovations to add bathrooms, etc, and often they were not built as hotels to start, so the rooms within a hotel are much less uniform than in the US).
The best ways to find them are to use a booking site such as Hotels dot com or Booking dot com, and specify a room for 3 people; or, if there's a hotel that interests you, e-mail them directly to ask for what you need. Just because Rick doesn't list triples at a particular hotel doesn't mean they don't exist. But be specific in your request: for instance, if you need 3 single beds, be sure to say so, or you may end up with a double bed and a single bed.