[dheeraj]

according to conditional probability the probability of some event A occurring is the same whether or not some other event B has been observed it is only when we present some outside condition C that the probabilities change
for example the probability of die A landing on 1 is 1/6 and the probability of A and B adding up to 7 is 5/36(condition C) therefore if we ask the probability of A and b adding up to 8 it is 5/36 if we ask given A is 1 the probability becomes 1/6 because only an outcome of 6 will give us the desired outcome

in your problem the chances of a song landing in the first half of the playlist are 1/2 and are equal to the chances of a song in the second half
the fact that the last 10 songs have been played is irrelevant as each time a new song is played it is chosen randomly and thus has 1/2 chance of being in the first half of the playlist
therefore the probabilities are equal