$($a$)$ Triple$-$DES is used to encrypt a message in CBC mode. Suppose that the ciphertext consists of $4$ blocks. What is the probability that we can find two identical ciphertext blocks?

$($b$)$ Triple$-$DES is used to encrypt a large file in CBC mode. The file size is $\backslash (2^\{35\}\backslash )$ bytes. Roughly what is the probability that we can find two identical ciphertext blocks? $($Remarks: one byte consists of $8$ bits.$)$

$($c$)$ AES is used to encrypt a huge message in Counter mode. The file size is $\backslash (2^\{64\}\backslash )$ bytes. All the bytes in the file have value zero. Roughly what is the probability that we can find two identical ciphertext blocks?