There are three tickets in the box, so the probability of 0 is 2/3 and the probability of 1 is 1/3.
After relabeling, the box has two tickets with "tails" and one ticket with "heads".
After relabeling, there are still three tickets in the box. The probability of tails is 2/3 and the probability of heads is 1/3: the probabilities have not changed, only the names of the outcomes are different.