Benfords Law of Words Background

Benford's Law is freaky!

Of all the numbers in the world, roughly 30% of them start with a 1! 17.6% start with a 2, 12.5% start with a 3, and so on, and so on.

For example, take a look at the following graph. Take the largest 120000 towns in the world, take their altitude, and voila - they obey Benford's law. Divide these numbers by ~3 to convert them into meters, and amazingly, they still obey this law!



In fact, it can be generalized past the first digit:



Source



Challenge

So I wondered, how does this apply to letters and words?

Your challenge is to parse the big list of words below and formulate the table above (printing a matrix will suffice). Unlike this work, you will not only need to find the occurrence of the first letter, but also the second, third, fourth, and fifth. If a word does not have the nth digit, you can ignore that word (i.e. if you are compiling the 5th column (looking at the fifth digit), you should ignore all words less than 5 characters long)  

Big List of Words: https://raw.githubusercontent.com/kevina/wordlist/master/alt12dicts/2of4brif.txt

Due to suggestion in the comments, this contest is now a code golf competiton, so shortest code in bytes wins. The entry must be a complete program and must output the table specified above. Built-ins are allowed.

Good luck!
Mathematica 246 bytes
The probabilities are based on all the words in the file.
p=Prepend;t=Transpose;d=&quot;Digit&quot;; 
p[t[p[N[#/Total@#,5]&amp;/@ t[Sort[Cases[Tally[Position[Characters
@Import[&quot;t.txt&quot;,&quot;List&quot;],#][[All,2]]],{n_,_} /;n&lt;6]]/.{_,k_}-&gt;k&amp;/@
(c=CharacterRange[&quot;a&quot;,&quot;z&quot;])],c]],{d,&quot;1st &quot;&lt;&gt; d,&quot;2nd &quot;&lt;&gt;d,&quot;3rd &quot;&lt;&gt;d,&quot;4th &quot;&lt;&gt;d,&quot;5th &quot;&lt;&gt;d}]
//Grid




In the given list of 60387 words, the occurrences are distributed as follows. Letters &quot;s&quot; and &quot;c&quot; are the most likely to appear at the beginning of a word (7455 and 6008, respectively). Only 11 words begin with the letter &quot;x&quot;.


Without headers in table  162 bytes
t=Transpose;t[N[#/Total@#]&amp;/@t[Sort[Cases[Tally[Position[Characters@Import[&quot;t.txt&quot;, &quot;List&quot;], #][[All,2]]],{n_,_} /;n&lt;6]]/.{_,k_}-&gt;k&amp;/@CharacterRange[&quot;a&quot;,&quot;z&quot;]]]//Grid