Let us suppose to have a box with a button. This box contains an unknown number of white balls.

When I push the button a white ball is ejected. Then I take that ball and put it in the same box. Now, what is the probability that next time that I push the button the very same ball is ejected?

My opinion is since I do not have any way to estimate this probability (I do not know the balls number in the box) the only way is to consider favorable outcomes over possible outcomes: {the same ball}/{the same ball + another ball} which is 1/2.

Many people do not agree with me, but nobody is able to provide me a different way to estimate this probability. Essentially for most of them is higher the probability to have more than two balls in the box, so the probability to get the same ball is less than 1/2. I disagree with them because we have no information about the balls in the box.

Can somebody help me? either proving me that I am wrong or providing me a way to prove that I am right.