fresh vegetable juice

I would go with...........basically the same calories that were in the carrot originally.

Juicing can remove fiber (a healthy good for you nutrient). There are 2 types of fiber; soluble & insoluble and calorie counts vary. Juicing leaves the soluble fiber in. But if you google fiber calories there is no clear consensus as to calorie counts for soluble vs. insoluble.

Or you could just use calorie counts for a commercially produced carrot juice, on the assumption that carrot juice is carrot juice.