In case of 4 people, the immediate neighbours of the starter each have a starting probability of 1/2 of not being the last.
For the one opposite, it does not matter whether the first toss is heads or tails. After the first toss, he also has a probability of 1/2 of not being the last. So his effective starting probability is also 1x1/2 = 1/2
All have equal probability of getting the coin before the last person.