Suppose you are throwing coins and asking what is the probability of heads coming before tails.
Now let's change that questions so that you throw the coins and say what was tossed, heads or tails, and the question is what did you say first, heads or tails.
Now let's add to the second variant that every minute you also say what the time is. So you are now saying "heads", "tails" or the time. Saying the time will not change the probability of the heads or the tails. Similarly, the fact that there are black balls and you now say that you picked one out, will not change anything. The question is, what will you say first "red" or "white".
In other words, the question is what is the probability that out of the red and white balls the first one you select is red. That is 3 possibilities out of 7.