A box contains three coins with different probabilities of landing on Heads: $P(H_1) = 0.5$, $P(H_2) = 0.6$, and $P(H_3) = 0.8$. A coin is chosen at random from the box and flipped twice. Given that both flips result in the same face (either both Heads or both Tails), what is the probability that the chosen coin was the third coin?