Maybe Darius was also a believer like Cyrus. Or maybe he saw the archives of Cyrus’ activities and thoughts and observed that his predecessor acknowledged the God of the Hebrews as The Great God and credited Him with his victories and safety.
Again, if one can capture his thoughts, the future generations should be thankful to find it. No one else can know why a person is or was whatever he is or became and learn from his experiences except the man or woman passes on his thoughts.
I wonder if any prophecies were made about Darius.