The probability of the second person drawing is also (10/1) * (110) =1.
The probability of the third person winning is 0. Suppose he is here, taking a black ball from the box, and the probability of not winning the prize is 1.
The probability of the fourth person being drawn is (10/1) * (9/10) *1* (1/8) = 9/88 > 8/88.
So the first person really lost.