There are such 11 letters. So there are 11^4 of four-letter strings.
The symmetric string are those in which the third letter is the same as the second and the fourth is the same as the first. So the first two letters determine such a string. There are 11^2 ways to choose first two letters.
So the answer is 11^2/11^4 = 1/11^2 approx.= 0,0083.