The best book agents can get as many as 1,500 queries per month, and they sometimes only offer to represent approximately 6 new clients per year. Of those 6 new clients, 3 will most likely have been published elsewhere already. So, in a calendar year, a top agent may receive as many as 18,000 queries and represent as few as 3 unpublished authors from that pile! Others are more optimistic, saying that an unpublished author has a 1 in 500 chance of finding representation.” [source: here] . If you do the Mathematics, that is as likely as if you are standing in a crowd of 6,000 people at a concert and you get picked from that group to come on stage. In other words, 99.97% of submissions are rejected. Ouch!
Here’s another take on the subject. “According to Heather Hummel, founder of PathBinder Publishing, only 4% of the query letters sent to agents get a positive response. Of the approximately ten million proposals sent to agents and editors, only 65,000 become books. That’s 0.0065% of all book proposals being accepted. Not even 1/10th of 1%. Yikes!
Conclusion 1. It’s incredibly difficult to gain an agent’s interest, and 2. It’s incredibly difficult to get published in the traditional way.