There is really no difference between the modals may, might and could when you’re expressing possibility.  In the following examples, you can substitute any of these three modals.  The verb that follows these modals is in the simple form.

May:

Examples:
They say it may rain tomorrow. (It’s possible that it will rain.)
The jury may decide that he’s innocent.
That may be true, but I don’t think so.  (It’s possible that it is true.)
(Note: may and be are both verbs, but maybe is an adverb and cannot be used in this sentence.)

In the negative, may not means that it’s possible that something is not true.

Examples:
They may not be in the classroom now.  (It’s possible that they aren’t in the classroom now.)
It may not work, but you can try.  (It’s possible that it won’t work.)
(Note:  The negative of may is never mayn’t.  It is always may not.)

Might:

Examples:
I might be late for the meeting tomorrow.
He might have some extra money he could lend you.
It might snow this Saturday..

In the negative, might not means that it’s possible that something is not true.

Examples:
He might not know the answer.  (It’s possible that he doesn’t know the answer.)
Her mother said she might not come to the party.  (It’s possible that she won’t come to the party.)
(Note:  In standard English the negative of might is might not, not mightn’t.)

Could:

Examples:
She’s not here yet.  She could be stuck in traffic.
This blog could make you famous.
This could take a while, so come back tomorrow.

In the negative, could not has a different meaning than may not or might not.  It means that it’s impossible that something is true, NOT it’s possible that something isn’t true.

Examples:
He could not remember her name.  (It was impossible for him to remember her name.)
We couldn’t stay long because we had to study for a test.  (It was impossible for us to stay long.)

Must be and have to be are used for a strong possibility.  They are used when making a strong guess based on evidence.

Must be:

Examples:
You’ve been driving all night.  You must be tired.  (evidence = you’ve been driving all night.)
He’s not at work this week.  He must be on vacation.  (evidence = he’s not at work.)
She must be in love.  I’ve never seen her so happy.  (evidence = she’s so happy.)

In the negative, must not is used for a negative guess based on evidence.  It can be used with verbs other than be.

Examples:
I must not be very smart.  I can’t figure out this problem.  (evidence = I can’t figure out this problem.)
I called her, but she didn’t answer.  Her phone must not work.  (evidence = she didn’t answer.)

Have to be:

Examples:
He has to be crazy to make the same mistake again.
They have to be very thirsty after their long walk in the sun.
I have to be out of my mind to listen to you again.

In the negative, do/does not have to is no longer about a guess based on evidence.  It is about not being necessary.

Examples:
He doesn’t have to help clean up.  (It’s not necessary for him to help clean up.)
We don’t have to go to school today.  It’s closed.  (It’s not necessary for us to go to school today.)