The probability of picking a specific letter when there are \( N \) letter tiles in a box, assuming that each letter is equally likely to be picked, is given by the equation:
\[ P(X) = \frac{1}{N} \]
This indicates that the probability of selecting any particular letter \( X \) is one out of the total number \( N \) of letters.
Therefore, the correct response is:
\[ P(X) = \frac{1}{N} \]
or
\[ P\left( X \right) = \frac{1}{N} \]
These two notations are equivalent and represent the same concept.