It sounds a bit abrupt in the first sentence, but I can easily imagine the other two sentences being used without the definite article without causing any commotion.
#1 - I am greatest at guessing people's ages. (Sounds arrogant though with all due respect to M. Ali.) What does "with all due respect to M. Ali" mean? Thank you very much for your reply,
The boxer Muhammad Ali had several catchphrases, one of which was "I am the greatest!"
The speaker in your question means that "I am (the) greatest" sounds arrogant; he then "remembers" that M. Ali used to use the phrase, and shows due deference by adding "with all due respect to M. Ali" – in other words, "I don't of course mean to imply that M. Ali was arrogant!"