Conditional probability is about calculating the probability of an event given that
another event has already happened.
Suppose I want to calculate the probability of getting at least 2 tails in 3 coin tosses...
The unconditional probability is 0.5 because there are 4 ways of getting 2 or more tails: TTT, TTH, THT, HTT; and four ways of getting less than 2 tails: HHH, HHT, HTH, THH so 4/8 = 0.5
But the conditional probability of getting two or more tails in 3 tosses GIVEN that at least one turns up tails is 0.75 because there 3 ways of getting at least 1 tail on the two remaining tosses: TH, HT and TT as opposed to only 1 way of getting no tails: HH.
We could write that P(A|B) where event A would be getting at least two out of three tails and B would be the condition that at least one toss turns out tails
But to write P(A|A) - apart from making no sense - would express the probability of event A occurring given that event A occurs - or in the coin toss thing - getting at least two tails given that we get at least two tails...and that can only ever be exactly 1.
Unless you are asking us to place ourselves prior to the composition of Beethoven's symphony and (pretending that we do not know that this is a universe that has produced Beethoven's symphony) calculate the odds from that perspective (which of course we couldn't possibly), what you are asking is for us to calculate the odds of a universe that has produced Beethoven's symphony (being as it is the only universe we know about) producing Beethoven's symphony given that it is a universe that has produced Beethoven's symphony.
The answer is still 1 - I'm sure of that - but I still don't understand the question!