What is the difference between Probe and Prove?

What is the difference between Probe and Prove? :

Probe : (noun)

1 ) Thorough and careful investigation of something

There was a probe into the disappearance of government funds.

2 ) Tool for examining a place which can not be reached otherwise especially a thin implement with a blunt end used by a doctor for examining a wound

Probe : (verb)

1 ) Explore or examine something with or as if with

A probe

He probed the swelling anxiously with his fingers.

Search lights probed the right sky.

2 ) Investigate or examine something closely

She tried to probe my mind to find out what I was thinking.

The journalist was probing into several financial scandals.

Prove : (verb)

1 ) Show that something is true or certain by means of argument or evidence

Prove that he is guilty.

Can you prove it to me?

I shall prove to you that the witness is not speaking the truth.

2 ) Turn out to be something

Be seen or found to be something

The old methods proved best after all.

The task proved to be more difficult that we had thought.

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