For your question, I think the following methods are more appropriate.

Classical definition of probability If an experiment meets two conditions:

(1) The experiment has only a limited number of basic results.

(2) The possibility of each basic result of the test is the same.

Such an experiment becomes a classic experiment.

For event A in the classic experiment, its probability is defined as:

P(A)=m/n, where n represents the total number of all possible basic results in the experiment. M represents the number of basic test results contained in event A. This method of defining probability is called the classical definition of probability.

Originally, the two balls in the box were not connected with the balls put in later, but when one ball was taken out, the white ball was connected (because it might be the original white ball).

Starting from the definition of probability, calculate all possible events (at least one of the three balls is a white ball), and calculate the events including (three balls have two white balls).

The total possibility of three balls and at least one white ball is white, white black and white black. three

Three balls have two white balls, and the total possibility is 1.

So the probability of 1 white ball is 1/3.

Here, the original condition of having a white ball is understood as only 1 white ball.