Rainbow Drops
This information pertains to Rainbow/Mythic item drops.
Information taken from the forums as posted by Stephen, referencing build 110 in this forum post
The information below is specifically based on solo player vs. a boss on normal difficulty.
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Boss Drops
Most bosses will do three passes on an item generator called LegendIG. This generator will create a mythic item 1 in 300 times for players below level 90.
At level 90, this generator will create a mythic item 1 in 100 times. This means that you have a 3 in 300 chance to get at least one mythic when fighting bosses at level 90.
Boss Treasure Chests
The treasure chests found after a boss fight have a 1 in 500 chance to generate a mythic item until you reach level 90 where the chance is increased to 1 in 250.
HDoL Bosses
Bosses in the Horrific Dungeon of Legend also do three passes on the LegendIG. Their chance to drop a mythic is 1 in 100 until level 90 when it increases to 1 in 60. With three passes that gives you 3 in 100 or 3 in 60, depending on level.
Summary
Playing solo on normal is the worst case for getting mythic drops. Until level 90 you'll have a 1 in 100 chance to see some mythic drop when you kill a boss. After level 90 you'll have a 1 in 33 chance to see some mythic drop when you kill a boss.
The drop rate of course can be adjusted by increasing difficulty and subsequently the loot modifier you see on the tooltip for monsters. Playing with more folks at a higher difficulty will increase your chances quite a bit.