I have a continuous time series signal $x$ (financial data varying with time) where the values of $x$ are exponentially distributed. The random variable $x$ changes with time, however, we assume that the probability distribution p(x) is time invariant. I am observing $x$ in real time and let's say that right now, at time $t$, it has taken a value $x \geq X_t$. I am now interested in calculating the probability that x will take a value $x \leq X_{t+T}$ at an arbitrary future point in time, $t+T$, given that we know its current value. So, mathematically I think I am interested in calculating this probability:
$$p(x \leq X_{t+T}~|~\geq X_t)$$
I have attached a drawing of this scenario below for ease of illustration. Essentially what I am asking is, given that I have observed that $x$ is currently in region #1, what is the probability that $x$ will end up in region #2 at some point in the future? Additionally, is there any possible method I can estimate the time $T$ it will take to reach region #2?
I thought of using Bayes theorem to evaluate the probability above, however, from my knowledge Bayes theorem looks something like this:
$$ p(A~|~B) = \frac{p(A~\cap~B)}{p(~B~)} $$
In my case I don't understand how I can evaluate $p(A~\cap~B)$ because the two regions I am interested in do not intersect.