Missing Ball

John's teacher decided to give a prize to two of her 20 students. She placed 20 balls numbered from 1 to 20 in a box and then randomly assigned a distinct number from 1 to 20 to each student. She intends to draw at random 2 balls from this box and give a prize to the two lucky students.

She drew a ball, but the ball fell from her hand and got lost. Nobody knows what the number on this ball was. Then the teacher decided to proceed with the draw using the 19 remaining balls. What is the probability that John wins the prize?

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