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?      

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.
