The FBI thought Huma Abedin’s laptop computer had evidence of she and her boss, former Secretary of State Hillary Clinton, mishandling classified information, according to a search warrant released Tuesday that shows the basis agents had for upending the presidential election with their election-season probe.

Agents were also hoping to see if anyone had used the laptop to hack into Clinton emails, according to the affidavit agents filed to justify the warrant.

Ms. Abedin, one of Mrs. Clinton’s top aides from her time in the State Department and again on the campaign trail, had shared the laptop with now-estranged husband Anthony Weiner. The FBI seized the laptop in a probe of Mr. Weiner, but discovered it also had messages between Mrs. Clinton and Ms. Abedin.

“There is … probable cause to believe that the correspondence between them located on the Subject Laptop contains classified information which was produced by and is owned by the U.S. Government. The Subject Laptop was never authorized for the storage or transmission of classified or national defense information,” the FBI said in the affidavit.

FBI Director James B. Comey sent shock waves through the presidential election in late October when he announced, just months after clearing Mrs. Clinton of criminal wrongdoing in her handling of classified emails, that he was reopening the probe based on new information.

That information was the discovery of Ms. Abedin’s messages on the shared laptop, a Dell Inspiron with a 1-terabyte hard drive, which agents already had while investigating Mr. Weiner for possible illicit sexual messages with an underage girl.

Agents then obtained a new search warrant on Oct. 30 to check the laptop in connection with the Clinton email probe.

After a brief legal battle, Judge P. Kevin Castel ordered the warrant made public Tuesday.

The warrant doesn’t shed very much new light on what agents found, but Mr. Comey said none of if changed their initial finding in the case that Mrs. Clinton did mishandle classified information and did put national security at risk, but was too technologically inept to know the risks she was running and thus should not be criminally charged.

Democrats have blamed the late-season announcement for derailing Mrs. Clinton’s campaign, and she lost in a squeaker to GOP candidate Donald Trump.

The Obama administration had at first opposed releasing the search warrant but dropped its objection last week, instead only asking that certain names be redacted.

In Tuesday’s documents, the name of the FBI agent requesting the search warrant is blacked out.

Also redacted are the names of two other people who appear to be Ms. Abedin and Mr. Weiner. Mrs. Clinton’s name does appear. Judge Castel said in an order Monday that her involvement has been publicly established, and it made no sense to keep her name out of the documents.

Even with the election over and Mrs. Clinton returning to private life, her emails are still very much in the spotlight.

The State Department continues, under orders from federal courts, to release some of the thousands of new messages that the FBI recovered during its initial probe. The next releases are due Jan. 3 and 4.

As of the last court update, the FBI had yet to turn over to the State Department any of the emails obtained from the Abedin computer.

The department is now battling with Judicial Watch, which says those new emails from the Abedin computer should be released as part of a current open records lawsuit. The State Department insists Judicial Watch should file a new Freedom of Information Act request instead.

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