Found this...says 9000 or more applications for elk, moose,and sheep. 3 tags for sheep so odds may be 1 in 3000 if 9000 apply for sheep or maybe the 9000 is total big game apps so is more like 1 in 1000 odds.
"Between 9,000 and 12,000 people apply for the big three tags, depending on the year and the species.
For instance, Williams said, the odds of drawing into a bull moose tag are one in 700 or 800 depending on the year."