What is the probability a person sees a tree by looking out of the window? I'm familiar with the basic probability rules which problems come in the form of:

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*What is the probability of getting a head next by tossing a coin? 0.5

*What is the probability of getting a 3 if a number is chosen uniformly at random from the set {1, 2, 3, 4}? 0.25

How more complicated forms of questions are calculated? for example: what is the probability a person sees a tree by looking out of the window given there are 2 trees that could be seen from that window?
There are many things to consider:

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*The person's eye vision.

*Time of the day (and how many light bulbs are around in case it's after sunset)

*The direction at which he looks.

*How tall are the trees?

*Can the person pass a drug test at the given moment?

*Does he have a history of delusions?

And the list goes on which may contain infinite possibilities leading to seeing / not seeing a tree. Given we don't have a frequency of people who saw a tree by looking from that very same window, how to calculate the probability with any degrees of accuracy? How confident are we given that we are 100% confident the probability of getting 3 out of {1, 2, 3, 4} is 0.25? What if we don't have anything given in which case the question is the same as the title?


There are many things to consider [...] And the list goes on which may contain infinite possibilities leading to seeing / not seeing a tree.

If you want to consider even extreme cases like someone being delusional, then as you noticed, there is an infinite number of possibilities, so the the answer is simple: the probability is zero. It is something divided by infinity, so it approaches zero.
The calculation is pretty useless because the question is too broad. That is why we usually simplify such questions limiting the scenarios to consider (for most use cases you probably can ignore delusions, etc). Not seeing a tree because of being blind is a different thing than because of living in the desert.
