Is a miracle still a miracle if it took a long time for it to happen? Suppose $t=0$ to be the moment of Big Bang. From then on an event has been "trying" to happen every second. The probability of it happening in a time duration of $1s$ is $10^{-10}$. And this probability 'resets' every second. So the probability of it happening in the time interval $t=0$ to $t=1s$ is $10^{-10}$. It is again $10^{-10}$ from $t=1s$ to $t=2s$ and so on.
Suppose the event happens for the first time in the time interval from $t=10^{20}s$ to $t=(10^{20}+1)s$.
It took $10^{20}s$ for it to happen. The probability of it not happening in $10^{20}$s is $(1-10^{-10})^{10^{20}}\approx e^{-10}$ which makes the probability of it happening in $10^{20}s$ almost $1$. From this point of view,  it seems no 'big thing' that the event has happened in $10^{20}s$.
However, just before the event happened, we know from gambler's fallacy that the fact that it did not happen in the last $\approx10^{20}s$ is not going to affect the odds of it happening in the future. The probability of it happening in the next few moments is the same old $10^{-10}$. From this point of view, it indeed seems like a miracle that such an event of very low probability has happened.
 A: The probability that the event happens in the time interval $(10^{20},10^{20}+1]$ is $$10^{-10}$$
a very small number. It is a mirackle if it happens...
The probability that this is the first occurrence is$$\left(1-10^{-10}\right)^{10^{20}}10^{-10},$$
a very small number again. So, it is an even greater miracle...
On the other hand $$1-\left(1-10^{-10}\right)^{10^{20}}$$
is, indeed, very close to $1$.  But this is the probability that the event has happened at least once so far (until the $10^{10^{20}}$th moment), but not the probability that it happens now in the $10^{10^{20}}$th moment. 
Perhaps the argumentation above resolves the mistery.
So, we have three miracles:
(1) The event has not yet happened so far.
(2) The event happens exactly now and never before.
(3) It happens exactly now independently of the past.
Is there any contradiction?
To answer the question in the title of the OP.
Yes, it it is still a miracle that the event happens in a given time slot even if it is not a miracle that the even has taken place if enough time has gone by.
