What types of carbon fixation is least common for plants in arid locations?

The answer is a C3 fixation.

Plants are located in different regions with a different condition, so they had to adapt the carbon fixation. There are three types of carbon fixation in plants - C3, C4, and CAM fixation. C3 and C4 plants open their stomata during the day while CAM plants open stomata during the night.
Plants in arid locations use CAM carbon fixation because of adaptation to water deficiency. In CAM plants, stomata are closed during the day and water loss is reduced. In the night when is colder, stomata open and carbon dioxide enters through stomata. In C4 carbon fixation, there is also adaptation to high temperatures thanks to enzymes that increase the rates of photorespiration, unlike the C3 fixation.