What is abnormal evidence in the play, Riders to the Sea, which it contributed in creating the tragic atmosphere?

I'm not sure what you mean by "abnormal evidence." In Riders to the Sea, the matriarch of the family, Maurya, is gifted with second sight - a gift commonly known throughout Celtic regions. Second sight is a natural occurrence and few doubt the visions seen by those who have the gift, as is the case with Maurya when she comes home to describe the vision she's had.

Maurya had gone down to the spring well to wait for Bartley to pass so that she could wish him God speed and give him a chunk of bread wrapped in cloth, but when he rides past on the red mare, she is unable to speak a word. The gray pony follows him, ridden by Michael - a son she is convinced is already dead. She saw him wearing new shoes and fine looking clothes and in that moment knows that she will lose Bartley as well.