Add to the 1d10 roll the number of ranks your Intuition is above Typical (ex. Incredible is four ranks above Typical [GD, EX, RM, IN] so +4).
In case of ties, the character with the higher Intuition goes first.
To notate that, each character's Initiative is listed as a decimal number with the first part (left of the decimal point) equal to their 1d10 roll plus the number of ranks their Intuition is above Typical. The second part (right of the decimal point) is equal to just the number of ranks the character's Intuition is above Typical (Typical Intuition or less is signified by a zero).
For example, character A has Excellent Intuition (2 ranks above Typical) and rolls an 8. Her Initiative is 10.2 (8+2 followed by a decimal followed by 2).
Character B has Good Intuition (1 rank above Typical) and rolls a 9. Her Initiative is 10.1 (9+1 followed by a decimal followed by 1).
Character A goes first because, although the total of the die roll and Intuition modifier is the same (10) for both, character A has a higher Intuition, as signified by the 10.2 as opposed to the 10.1.
Actions are resolved in order from the character with the highest Initiative total to the character with the lowest.