The words "surely" and "certainly" are very close in their meaning.
Both words are used when there is no doubt. They have their roots in words that mean "secure" and "reliable".
A man might say to his girlfriend, "I certainly love you" when he has no doubt.
The woman might say, "he surely loves me because he is so thoughtful and kind".
The word "definitely", however, has its roots in a word that means specific, precise and exact.
If a man says to his wife, "I definitely love you" it will not have the same emotion.
Hope this helps