The probability of picking any specific letter from a total of N letter tiles, assuming each tile is equally likely to be picked, is given by the formula:
\[ P(X) = \frac{1}{N}. \]
This is because there is 1 favorable outcome (picking a specific letter) out of N possible outcomes (total tiles).
Therefore, the correct equation representing the probability of each possible outcome in a trial is:
\[ P(X) = \frac{1}{N}. \]