If each competitor’s draw remains secret until all the balls have been drawn then each person has an equal probability of drawing the black ball, in this case 1 in 20 or 0.05.

To see why, think about the situation where all participants reach into the bag simultaneously and grab one ball at random. While their hands are in the bag, nobody knows who has the black ball and each participant has the same chance of holding it. The situation where one person draws at a time is essentially no different as long as their draw remains secret until all balls have been drawn.