story identification - Looking for a book about a human-nature predicting supercomputer

I am looking for the name of a book (might be a short story) which I have read many years ago. The general plot as I remember it:

There is a supercomputer which can predict with good accuracy the human actions in the next several days (after that, it is just less accurate).

The computer could alert the police of future possible crimes, and would.

The computer alerted the police that a man is going to commit a murder, and the man is placed under arrest.

His son goes to a computer-interface station to ask the computer for help.

The computer sends the son on a complicated quest.

Spoiler alert: I am giving away plot-sensitive details at the end, so they're hidden below.

- The son kills the computer, and we find out that the murder-alert was actually on the son (but their system automatically redirects it to the parent's name, or just a wrong identification for Mr. Surname).
- We find out the computer planned the whole thing, because it got depressed after dealing with the pain and suffering of the whole human race.

Answer

From Wiki:

"All the Troubles of the World" is a science fiction short story by Isaac Asimov. The story first appeared in the April 1958 issue of Super-Science Fiction, and was reprinted in the 1959 collection Nine Tomorrows. It is one of a loosely-connected series of stories by Asimov concerning the fictional supercomputer Multivac.

The story synopsys matches your description to a T, including the end.

To confirm his suspicion, Othman asks Multivac a question never previously posed to the vast computer, "Multivac, what do you yourself want more than anything else?". Multivac's answer is succinct and unequivocal: "I want to die."

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