Good-Turing Smoothing Intuition
There are no unseen item types in the given data, by definition. 3 is the count of items seen once, and they are already included in the denominator 18. If the next item were previously unseen, it would become seen once when it appears. Since 3-of-18 examples were seen-once items, this is an estimate of the probability that the next item will be seen-once too on its first appearance.

It is certainly a heuristic. There is no way to know whether there are 0 or 1000 other types out there.