Empirical probabiliy: If an event has happened,how can there be any probabiliy? 
let there be $n$ trials of an experiment and $A$ be an event associated to it such that $A$ happens in $m$ trials . Thus the empirical probability  $$P(A) = \dfrac{m}{n}$$.
A coin is tossed $500$ times with head occuring $240$ times and tail $260$ times. What is the probability of occurence of each of these events? ....

So,if the experiment is done and we get the frequencies of the events,how can there be any probability? Probability measures the likelihood of how centainly the event will come. But here the experiment is done,and we have results, so how can there be probability? I know head has come $240$ times; then why the question of probability. Then what empirical probability measures?? The certainty of an event which has occured already?? Confused.
 A: The specification of the model is missing. You need something like: Event $A$ on a single trial occurs with probability $P_A$. 
You perform $n$ (independent) trials and observe $A$ $m$ times. So you have an empirical probability $P_{\rm{empirical}}(A)=\frac{m}{n}$.
Now you can ask about the relationship between $P_{\rm{empirical}}(A)$ and $P(A)$, or if you are philosophically so inclined ask what $P_{\rm{empirical}}(A)$ tells us about $P(A)$.
A: This might be more of a philosophical problem than not. Maybe even more suited to the physics stack exchange. Your issue is one of wording, not one of mathematics, at least.
The point is that you had some coin and you wanted to find out the (unknown) odds of flipping a heads or a tails.
So you performed an experiment and ended up with some number of heads and tails. So now you are able to look back at those numbers and see what the oddsmust have been in order for you to have seen them.
(Of course, you need to know the probability of seeing those numbers to begin with given various `true' odds, so in a physical problem you can only give the odds with some probability, but for this problem it's idealised anyway and just getting you used to applying a formula.).
Does that answer the question?
A: Well, the exceprt alone doesn't say all that's needed to make sense. It's possible other parts of the text could shed light on what that part wants to say.
I'll try filling possible blanks.
For once, you could say the probability of an event is what its empirical probability would be with an infinite number or trials (at least,  according to a frequentist interpretation, the one the excerpt seems to try to explain).
So, "probability" and "empirical probability" are two different things.
The particular experiment made gave you an empirical probability of 240/500 for heads.
The probability of the coin landing on heads (if the coin is fair), is 1/2, since in an hypotetical infinite experiment you would obtain heads exactly half of the times.
Worth noting is also what is an event: in this case, I think the text thinks of "landing on heads" as an event. You, on the other hand, consider the event "the coin landed on heads 240 times and on tails 260 times", and yes, the probability of that event is 1.
The difference is in the wording: landing vs landed, and usually in probability you consider "x-ing".  
In short, the excerpt alone doesn't explain everything. Maybe its context does?
EDIT: Ok I just saw what you added in a comment to the question. So yes, the context does: it's explaining the concept of probability from a frequentist standpoint. in here, it's trying to deduce the "probability" of the coin landing on heads from the experiment where heads came 240 out of 500 times, saying that you really can't. It will probably (ha) continue saying "but what if you could repeat the coin toss infinitely?" or something similar.
