Williams sat atop the rankings for 186 straight weeks before she was dethroned by Angelique Kerber earlier this month.
With Williams’ reign at the summit of the standings having come to an end, Halep feels that everyone has a better chance of winning tournaments and grand slam titles.
"It's much easier to believe in yourself when you see that Serena is not there anymore, like, winning every [event]," she said. “I feel that everything, it’s open now.
“I feel that everyone has a chance to win a big tournament, to reach No. 1. Everyone has a chance to reach the top if we believe. And we started to believe more, I think.”
Meanwhile, world No 3 Garbine Muguruza has admitted that she is glad Kerber is the new world number one as it marked the end of a period of pure dominance by Williams.
"I'm happy that we have a new face in the world number one, not because I have a preference, but just because I think it's good sometimes," she said.