Unable to understand notation regarding Shannon's theorem

$\underset{\mathcal{K}}{\text{Pr}}[\text{Enc}(K, m_0) = c]$ (and similarly $\underset{\mathcal{K}}{\text{Pr}}[\text{Enc}(K, m_1) = c]$) means the probability that $\text{Enc}(k, m_0) = c$, where you choose the key $k\in \mathcal{K}$ at random. Notice that, here, the values $m_0$ and $c$ are fixed, so what we want to know is, for these fixed $m_0$ and $c$, what is the probability that a uniformly random key $k$ results in encrypting $m_0$ to $c$.

As @fgrieu pointed out in the comments, the probability of a discrete event is simply the number of "favorable" cases divided by the total number of cases, so here it would be

$$\underset{\mathcal{K}}{\text{Pr}}[\text{Enc}(K, m_0) = c] = \frac{|\{k\in\mathcal{K} : \text{Enc}(k, m_0) = c\}|}{|\mathcal{K}|}.$$

PS: Sometimes we also add the randomness of the encryption algorithm into the equation. This is not that relevant for this discussion, but what this means is that you consider an encryption algorithm of the form $\text{Enc}(k, m, r)$, where $r\in\{0,1\}^\ell$ (for some $\ell$) is chosen uniformly random. Then you simply add $r$ as a subscript in the probability.