What do these notations mean in the definition of Perfect Secrecy, if we read those in English? If m: message, M: message space, k: key, K: keyspace, c: cipher, C: cipher space and $E_k$: encryption function, such that
$E_k(m) = c,\ m,m^* \in M,\ k\in K,\ c\in C.$

Then, what do the following notations actually mean in plain English?



What does it mean by $C=c$? If it means "If $C$ takes the value of $c$", to my understanding it is meaningless. Why would $C$ take the value of $c$? $c$ is a part of the whole message $C$. The same is true for $M$ and $m$.
Imagine the following three scenarios. In each, you intercept an encrypted message and you know from context:


the message is a randomly chosen key in $\{0,1\}^n$ for some other cryptosystem
the message is either "It's a boy!_" or "It's a girl!", both are equally likely
the message is a vote from someone in a referendum; it's either "yes" or "no_", and the probability of it being "yes" (based on your knowledge of that person's preferences) is around 9/10.


Each of these scenarios describes a different context and prior knowledge you may have about the message (formally: a probability distribution on messages). An encryption scheme that's any good won't reveal anything more about the encrypted message than you already know in any of these scenarios. Even in the last case where you can make a pretty good guess at the message without breaking any encryption, the ciphertext shouldn't tell you anything more than you already know.

The last line of that definition translates to "what you know about $m$ after seeing $c$ is the same as what you would know about $m$ without seeing $c$" (for any kind of knowledge about $m$ that you may have).