Gayle King: Surprised first lady didn't cancel

When Gayle King got to the White House to interview Michelle Obama Tuesday, "CBS This Morning" co-host was surprised to even be getting the opportunity.

The two are friends, King disclosed on the broadcast Wednesday.

And, King told fellow co-hosts Charlie Rose and Erica Hill, the first lady agreed to do the interview "because she wanted to support the launch, quite frankly. She was very excited about the show and she wanted to participate in the premiere. Lucky for us."

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But on Friday, King began thinking the interview wouldn't happen - because news broke of a controversial book alleging tension between Mrs. Obama and two top former aides to President Obama - and the first lady knew King would ask about the claim.

To King's delight, Mrs. Obama not only did the interview - she "answered every single question," including queries about the book.

What did King think of the book? Did she have firsthand knowledge of anything mentioned in it?

For more on the back-story behind the interview, click on the video above.