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<<<`grep -c $1`/${#1}

Test

>cat /usr/share/dict/words| ./test ulous
7.60000000000000000000

>grep -i ulous /usr/share/dict/words | wc -l
38

Python 3, 52 49 bytes

-3 bytes thanks to Kade, for assuming w to be the word list as list:

f=lambda s,w:w>[]and(s in w[0])/len(s)+f(s,w[1:])

Previous solution:

lambda s,w:sum(s in x for x in w.split('\n'))/len(s)

Assumes w to be the word list. I choose Python 3 because in my word list there are some Non-ASCII chars and Python 2 does not like them.

Perl 6,  45 36 33  32 bytes

wordlist as a filename f, 45 bytes

->$w,\f{grep({/:i"$w"/},f.IO.words)/$w.chars}

wordlist as a list l, 36 bytes

->$w,\l{grep({/:i"$w"/},l)/$w.chars}

using placeholder variables, and reverse (R) meta-operator, 33 bytes

{$^w.chars R/grep {/:i"$w"/},$^z}

using .comb to get a list of characters, rather than .chars to get a count, 32 bytes

{$^w.comb R/grep {/:i"$w"/},$^z}

Expanded:

{             # block lambda with placeholder parameters ｢$w｣ ｢$z｣

  $^w         # declare first parameter ( word to search for )
  .comb       # list of characters ( turns into count in numeric context )

  R[/]        # division operator with parameters reversed

  grep        # list the values that match ( turns into count in numeric context )

    {         # lambda with implicit parameter ｢$_｣
      /       # match against ｢$_｣
        :i    # ignorecase
        "$w"  # the word as a simple string
      /
    },

    $^z       # declare the wordlist to search through
              #( using a later letter in the alphabet
              #  so it is the second argument )
}