Based on my observation, after challengging Black Shrine Boss for several times, the drop rate of Embers of Hongik is :

10 % from calamity 1 bosses,

20 % from calamity 2 bosses,

30 % from calamity 3 bosses,

40 % from calamity 4 bosses,

50 % from calamity 5 bosses.

This is the statistic i purely made based on my experience. You have different thougts? Share it down below, i would love to discuss with you.