The law does not require probationary periods. However, employers are free to require  them and to set their own terms or conditions for what happens during them. An employer could elect to terminate anyone falling asleep at work, whether during a probationary period or not, and whether such nodding off is due to an injury or otherwise--the law does not require employers to keep employees who fall asleep or are inattentive at work. The law also does not require employers to allow employees a chance to present evidence in their favor. From what you write, what you employer did is legal, even if unfair.