# How to prove that a SKE scheme is IND-CPA secure

There's an IND-CPA SKE scheme 1 $(\mathsf{Gen}, \mathsf{Enc}, \mathsf{Dec})$. Scheme 2 is defined as $(\mathsf{Gen}', \mathsf{Enc}', \mathsf{Dec}')$, where $\mathsf{Gen}' = \mathsf{Gen}$, $\mathsf{Enc}'(k, m) = 0||\mathsf{Enc}(k, m)$ if $m\ne k$ and $1||k$ if $m=k$, $\mathsf{Dec}'(k, 0||c) = \mathsf{Dec}(k, c)$ and $\mathsf{Dec}'(k, 1||c) = c$. How do I go about proving that the scheme 2 is IND-CPA secure?

I'm also having trouble understanding if the adversary can guess the correct bit on a chosen plaintext pair given the ciphertext, given that when $m = k$ the ciphertext always starts with $1$, but for the scheme to be IND-CPA secure I know that the adversary should only be able to guess with negligible probability. What am I missing here?