Pete Rose knew Derek Jeter turns 40 on Thursday, which matches everything I’ve heard about baseball’s exiled Hit King. Even at 73, with the 25th anniversary of his lifetime suspension from Major League Baseball arriving in August, the non-Hall of Famer possesses the sharpest eye, the finest attention to detail, for the game that made him both famous and infamous. So even though he’s permanently on the outs due to a lack of honesty concerning his bets on baseball back in the day, you believe him when he pats himself on the back regarding Jeter, the active hit king (such a title gets you only lowercase letters) until he retires at year’s end. “I’m one of those guys who never thought he had a chance at passing me,” Rose told The Post Wednesday morning in a telephone interview. “He didn’t play last year, right?” “He played in 17 games,” I mildly corrected. “Go ahead and give him 200 hits last year and see where he is on the list,” Rose said. “He’s still 600 or 700 short. And tomorrow, he’s 40 years old.” Jeter began play Wednesday with 3,387 hits. If you add 188 hits to the 12 he actually tallied during his 2013 nightmare, that would give him 3,575 — 681 shy of Rose’s 4,256. Rose can say he told us so because he did just that at a time when it wasn’t in vogue to do so. On Oct. 10, 2012, the website Sports On Earth ran a piece quoting Rose on Jeter, just weeks after Jeter had led the American League with 216 hits at age 38.