There are 5 vowels out of 26 letters in the English alphabet. This leaves 26-5 = 21 consonants.
The theoretical probability of getting a consonant is 21/26 = 0.8077 = 80.77% approximately
Wayne found the empirical probability of a consonant as 60% which is quite a distance away from the 80.77% mentioned. The discrepancy is likely because vowels are tended to be used quite often in many words.
Words that are composed of consonants only are quite rare, but they do happen. Example: "fly" is a word with only consonants. I'm considering y to be a consonant.
