Get a word's individuality!
Bash, 41, 39, 34, 33, 26 bytes
EDIT:

Converted from function to a script
One byte off by removing the ignore case flag
Replaced wc -l with grep -c, saving 5 bytes. Thanks @Riley !

A rather trivial solution in bash + coreutils
Golfed
bc -l&lt;&lt;&lt;`grep -c $1`/${#1}

Test
&gt;cat /usr/share/dict/words| ./test ulous
7.60000000000000000000

&gt;grep -i ulous /usr/share/dict/words | wc -l
38