There are four tickets in the box originally, so each ticket has probability 1/4. The probability of HT is 1/4. The probability of TH is 1/4.
After relabeling, TT becomes 0, TH and HT each become 1, and HH becomes 2. There are still four tickets in the box. One of them (the former TT) has a 0, two of them (the former TH and HT) have a 1, and one of them (the former HH) has a 2.
The outcomes are therefore 0, 1, and 2. Their probabilities are 1/4, 2/4, and 1/4, respectively.
The probabilities have changed, because several outcomes that were originally distinct have been combined, through the relabeling, into a common outcome. However, the box still has the same number of tickets: relabeling cannot change that.