A bowler takes three wickets in three different overs and it was a hat trick. How did this happen?

Yes, it is possible and it was done by Merv Hughes against West Indies. He dismissed Greendige of the last ball of his over. And when he trapped LBW Patrick Patterson of his first ball of his next over, the innings of West Indies came to an end. After the innings of Australia and when West Indies came to bat for the second time, he dismissed Ambrose of his first delivery. Three consecutive wickets but a huge interval in between. Indeed a rare incident in the history of cricket.

At Perth, in 1988–89, Hughes completed a hat-trick spread across three separate overs, two innings, and two different days. He had Curtly Ambrose caught behind with the last ball of his 36th over; ended West Indies' first innings in his 37th, by removing Patrick Patterson; and more than a day later, completed his hat-trick by trapping Gordon Greenidge lbw with the first ball of West Indies' second innings.^[3]