Posterior probability of a coin given a head

Consider four coins labelled as $1,2,3$ and $4$. Suppose that the probability of obtaining a head in a single toss of the $i^{th}$ coin is $\frac i4$, $i=1,2,3,4$. A coin is chosen uniformly at random and flipped. Given that the flip resulted in a head, the conditional probability that the coin was labelled either $1$ or $2$ equals