Princess Eugenie announced her third pregnancy on May 4, and although she’s been staying out of the public eye since her father’s arrest in February, she’s been hitting the town ever since her happy news broke this week. Andrew Mountbatten-Windsor and Sarah Ferguson’s youngest daughter, 36, revealed her growing baby bump in a form-fitting black dress on Thursday, May 7, styling the outfit in two different ways for two very different events. The princess attended a press day for London's Fuse Communications, where guests browsed the latest kids' collections and enjoyed beauty treatments at the backstage salon and Bobbi Brown. Eugenie wore a silky black polka dot shirt buttoned up over her maxi dress and accessorized with her ever-present Sophie Lis mushroom earrings , which she has worn to nearly every public event since last summer. She also proved that the millennial-favorite green jacket is back, topping off her outfit with a new coat by Anine Bing.…