A lottery ticket(cupon?) with a row of 3 numbers. Those three numbers can vary from 0-9. A ticket(cupon) might be 5,6,7.

A number is picked randomly among the numbers 0-9. The number that was picked is then put back into the bowl. The lottery ends when it has three unequal numbers, for instance, it can pull out 5 numbers like this: "1,3,3,1,5", which leaves the lottery result with 1, 3,5 as the winning numbers.

What is the probabilty of winning then you have delievered a cupon consisting of the numbers 2,3,4?

My shot at it:

First number is always 1/9 chance.

Second number is 1/9*1/9 chance.

Third number is 1/9*1/9*1/9 chance.

This probability would be right if the lottery could have 3 numbers, no matter if a number got picked twice, or "trice".

Need a bit help