Solution: Total letters: 26. Vowels: 5, consonants: 21. Total 3-letter arrangements with distinct letters: $26 imes 25 imes 24$. Unfavorable cases (no vowels): $21 imes 20 imes 19$. Favorable probability: $1 - rac21 imes 20 imes 1926 imes 25 imes 24 = 1 - rac798015600 = 1 - rac133260 = rac127260$. $oxed\dfrac127260$