What is implied probability, in the context of universal codes?
The idea is the following: 

the following tree $T$

$
\\
\emptyset
\\ 
|   \ \setminus \\
|   \ \ \ \setminus \\
0 \ \ \ \ \   1
\\ 
|   \ \setminus \\
|   \ \ \ \setminus \\
00 \ \ \ \ \   01\\
\\ 
\ \ \ \ \ \ \ \ \ \ |   \ \setminus \\
\ \ \ \ \ \ \ \ \ \ |   \ \ \ \setminus \\
\ \ \ \ \ \ \ \ \ \ 010 \ \ \ \ \   011
$

of depth 3 is constructed by


Taking an object labeled as $\emptyset$ that has probability 1 and splitting it in half into two pieces which we label as $0,1$; who each acquire equal probabilities 1/2 individually.
Taking the object labeled as $0$ that has probability 1/2 and splitting it in half into two pieces which we label as $00,01$; who acquire equal probabilities 1/4 individually.
Taking the object labeled as $01$ that has probability 1/2 and splitting it in half into two pieces which we label as $010,011$; who each acquire equal probabilities 1/8 individually.


This is essentially the "unwrapping the Huffman algorithm in reverse." You are asking the wrong question, you should be asking "Why label it this way?"

The idea behind the Huffman coding scheme is that 


$0,1$ each cost 1 unit of "communication complexity" or "space complexity" depending on your interests
$00,01$ each cost 2 units of "communication complexity"
$010,011$ each cost 3 units of "communication complexity"


You should read chapter 5 of Cover and Thomas 

and this Wikipedia article on the kraft inequality is probably helpful too. however, if you want a proof of the infinite kraft inequality you need chapter 5 of Cover and Thomas. 

The idea is to continue this (type of) procedure unto infinity so that we get a something the following tree $T_\infty$

$
\\
\emptyset
\\ 
|   \ \setminus \\
|   \ \ \ \setminus \\
0 \ \ \ \ \   1
\\ 
|   \ \setminus \\
|   \ \ \ \setminus \\
00 \ \ \ \ \   01\\
\\ 
\ \ \ \ \ \ \ \ \ \ |   \ \setminus \\
\ \ \ \ \ \ \ \ \ \ |   \ \ \ \setminus \\
\ \ \ \ \ \ \ \ \ \ 010 \ \ \ \ \   011 \\ 
\ \ \ \ \ \ \ \ \ \ |   \ \setminus \\
\ \ \ \ \ \ \ \ \ \ |   \ \ \ \setminus \\
\ \ \ \ \ \ \ \ \ \ \vdots \ \ \ \ \   0101
$

which has infinite depth.  Each time you "split" a string, you maintain a "partition of unity" i.e., you maintain a probability distribution. The kraft inequality states that if your code was constructed in this manner, i.e.,
$$
\sum_{i : \text{leaf of }T_\infty} 2^{-l(i)} = 1 
$$
then the code is optimal.


  In other words if you have a set of binary strings $\mathcal{S}$ and the function 
  $$p(s) = 2^{-l(s)}$$
  turns out to actually satisfy the kraft inequality, i.e., 
  $$
\sum_{s \in \mathcal{S}} 2^{-l(i)} = 1, 
$$ then it is an optimal code. Therefore forming a probability distribution and being an optimal code are equivalent.


One can further prove that all such codes have a tree that witnesses their optimality.