I am having difficulties in understanding the racing vocabulary:-

1) There were 19 Contenders on the list.

2) There were 8 OFF THE TRAIL on a list that followed.

What is the meaning of Off The Trail ?

A quick Googling would have immediately told you that "off the trail" refers to the horses that are definitely not going to the Derby due to injury, illness, etc.

http://www.horse-races.net/library/derby-offtrail.htm