Chest 1:
100% for 4d5 epic rusty gilled mushroom (2d4/2 on EH/EN)
100% for a craftable item base table (this one is a large tree of subtables and I'll skip it)
2 x vendor trash lvl 28
0.5% for a ship amenity
1% for subtable 1 (none on EH/EN)
1% for subtable 2 (same on EH/EN)
1% for subtable 3 (none on EH/EN)

Subtable 1 (same on EE/EH/EN):
8% for epic spinal tap, epic leopar's chill, epic assassin's kiss, epic periron's talon, epic cranium cracker, epic sapphire sting, epic elemental bloom, golden orb of death
26% for subtable1-1 with more items (crab shield, epic leverage, epic thrall of the fire temple)
(oh boy... you are going to get great crossbow & wraps with mythic shield bonus in addition to mythic weapon bonus - unless I miss some check)
10% for subtable1-2 with same items except with +4 mythic bonuses instead of +2 and same bugs (9% per item, 28% for subtable with crab shield, great crossbow & wraps)

Subtable 2:
EE:
99% for 1 epic red cage mushroom
1% for 1 epic octopus stinkhorn mushroom
EH:
33% for subtable 1 (above)
33% for 1 epic red cage mushroom
3% for 1 epic octopus stinkhorn mushroom
EN:
10% for subtable 1
10% for 1 epic red cage mushroom
1% for 1 epic octopus stinkhorn mushroom

Subtable 3 (EE only):
4% per +6 to +7 stat tome or nothing

Ok... seems like in this chest the chance for tome on EE is 1%*24% = 0.24% or 1 in ~417 runs.