ABC News’ Barbara Walters has won the Hillary sweepstakes, snaring the first book-tour interview with Sen. Clinton about her White House memoir.Interview will air during an hourlong, primetime special on June 8, one day before Clinton’s “Living History” hits the stands. The special will air at 7 p.m. EDT, preceding the third game of the NBA finals. On the West Coast, the Walters’ special will air immediately following the playoff game. Insiders say Clinton tapped Walters based on a similar interview granted to Walters upon publication of her earlier book, “It Takes a Village” (1996). Clinton’s new book is being published by Simon & Schuster.