Let's say that a professional basketball player practices his shot.
- He scores with an average of 40%.
- Everytime he misses/scores he tries to readjust his shot.
Given that he misses the first 3 shots, is the probability of scoring the next one $1-0.6^3=0.784$ due to his adjustments or it remains $0.4$? If the first probability is correct, what happens if he scores in the next one? Will the probability to score be $1-0.6^2=0.64$?
This looks like the (in)famous Gambler's Fallacy: the (mistaken!) thinking is that if at any time you are below (or above) your normal average, then the next event will have to pull you back towards that average.
However, think of a fair coin that you flip. Is it possible for it to come up heads three times in a row, even though it is a perfectly fair coin? Sure! But given that it is a perfectly fair coin, the next flip has a $50$% chance of being heads and $50$% chance of being tails, just like any other time you flip that coin. As statisticians like to say: 'coins don't have memory'
Now, I know your objection, and in fact this is what your question is really about: isn't this person going to make adjustments? Indeed, given that we're dealing with a human being, who do have memory, and given that this person missed a bunch of shots in a row, isn't this person going to make adjustments?
Well, yes, that is quite possible ... but if the person is going to make adjustments, then all bets are off as far as what the probability is of this person making the next shot.
That is, if the person does not make adjustments, then the chance of making the next shot is $40$%. If the person does make adjustments, then we can't say anything at all about the probability of making the next shot.
Indeed, as such, I would think your assumptions are not very well defined: if this person keeps adjusting their shots, then their shooting average really becomes a moving target, so I don't think you can say it's $40$%. I suppose you could say that in the long term it is about $40$%, but even then, not knowing the nature of the adjustments, we really can't say anything about the percentage of the next shot being made. Maybe the person makes only very slight adjustments ... or maybe the person makes very big adjustments ... both kinds of adjustments could lead to a long-term average of about $40$%, but you can't say anything about the percentage of the very next one shot.