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:

*

*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:

*

*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?

Consider the probabilistic subject
$$
\text{prob}(H | I)
$$
i.e. "the probability that $H$, given that $I$". Here $H$ and $I$ are meaningful propositions, and $I$ must be not necessarily false.
For some such pairs $(H, I)$, we cannot evaluate the subject. e.g.
$$
\text{prob}(\text{dogs are risible} | \text{it will rain next Tuesday})
$$
Now consider your subject:
$$
\begin{align}
\text{prob}(&\text{a person sees a tree by looking out of the window} | \\ &\text{there are two trees that could be seen from that window})
\end{align}
$$
You haven't supplied enough information to calculate the probability, so your subject falls into the same category as my example involving dogs and rain. That's the end of the matter.
To make some quantitative progress, we'd have to add information that gives rise to symmetries in the situation which enable us to assign probabilities. For example, let $I$ be:

*

*There are two trees outside.

*Each time Bob glances out the window, he sees tree 1 with probability 0.3, and if he sees tree 1, he sees tree 2 with probability 0.1, and if he doesn't see tree 1, he sees tree 2 with probability 0.4.

*Bob takes two glances out the window.

and let $H$ be "Bob sees tree 1 or tree 2 or both". Then we could calculate the probability.
The business of forming probabilistic subjects that are relevant yet amenable to calculation, and evaluating them, is essentially the whole subject and art of probability!
