Can we predict the past? Can we use probability rules to predict the occurrence of an event which has already happened in the past or already formed? 
For example, hemoglobin is a protein formed of $141$ amino acids connected like a chain with specific order, the first amino acid is Leucine (we have only $20$ types of amino acids forming any protein), is it valid to say that probability of leucine being first in this chain is $\frac1{20}$ so the probability to get the $141$ a.a hemoglobin with such order by chance is $\left(\frac{1}{20}\right)^{141}?$ or this prediction makes no sense as we already have hemoglobin formed with such order in the nature?      
 A: That doesn't quite make sense. Your $\big ( \frac{1}{20} \big )$ tells you the chance that any uniformly (or with other known distribution) random amino acid chain starts with the same amino acid as hemoglobin (assuming the process of formation is uniformly random, which it probably isn't). Probability theory tells you about unknowns. It doesn't matter if these unknowns are already formed, like amino acids or marbles in an urn, or if you are predicting the probability that any chain that forms in the future will start with leucine.
A: The probability involved in these proteins/amino chains are much more complicated than simple probability rules.  
But if you are asking about past occurrences related to probability, for example, a coin flipped in the dark and covered up, or the same with a set of dice rolled under a box, the same probabilities apply to what's under there as do to future flips or rolls.  If that is what your are asking.
A: Probabilities can represent a state of limited knowledge of events that have
already happened. This can occur, for example, in games of cards after the
hands have already been dealt but before players have revealed their cards through play.
Each player has perfect knowledge of his or her own hand but only probabilistic
knowledge of the cards held by other players.
So we could say, given certain conditions, but not knowing what proteins these conditions
would give rise to, what is the probability that the conditions would give rise to hemoglobin?
The conditions that yield the answer $\left(\frac{1}{20}\right)^{141},$
however, would be something along the lines of we choose exactly $141$
amino acids one at a time from a practically infinite "bag" in which each
amino acid occurs with equal frequency.
Moreover we assume only one attempt.
That is not how proteins form under any realistic circumstances.
There were undoubtedly a great many times that hemoglobin could first have been
encoded by some creature's DNA during the history of life on Earth.
So even without taking into account the probabilistic
dependencies that may exist between the encoding of one amino acid
in a protein and the encoding of the next,
the probability under the limited one-time uniform-random-choice
conditions does not seem to be of much interest.
A: If you randomly deal a deck of 52 cards, 13 cards per person for four people, the probability of that particular deal is $1$ in $53,644,737,765,488,792,839,237,440,000\approx 2^{96}$. And yet, somehow people continue to play bridge, in spite of the low probability of each of the deals they play.
If you are trying to somehow use the complexity of hemoglobin as evidence that evolution was not purely random, or even that evolution does not occur at all, then this is poor evidence. Hemoglobin did not spontaneously occur, in evolution theory. Rather, proteins like hemoglobin occurred over time, and the more effective ones were selected for.
In particular, it is much easier to "evolve" hemoglobin than it is to randomly assemble it, since various intermediate simpler proteins are useful for survival. The random process begins to resemble more like a random search, trimming away the useless parts of the tree. 
And, of course, there might well have been umpteen gazillion different proteins that ultimately could serve such a function. Evolution on another world might well evolve a different complex of proteins, or a different type of chemistry altogether.
So, it is highly unlikely that hemoglobin would spontaneously generate at any particular point in time. That almost goes without saying. But nobody is saying this is how hemoglobin was formed.
