Is the supplication of a person accepted who supplicates to God for something he desires, but feels a strong presumption that it will not happen, and does this lack of certainty affect the response to the supplication?

What is forbidden is usually supplicating for the impossible. However, if the matter is probable, even if slightly, and not impossible, then supplicating for it is neither forbidden nor an act of aggression in supplication. Therefore, there is no sin upon you if you supplicate with this, even if you strongly believe it will not occur.

You should be confident in Allah's bounty and generosity when supplicating, and certain of a response. This does not contradict the possibility of the thing not occurring, as long as it is possible. The occurrence of the supplicated-for thing is not a condition for the response, as there are different forms for the response to a supplication.