How rare is a zombie with an enchanted shovel?

One day I was trying to make a house when loads of zombies come next to me and tried to kill me. Then all of a sudden I saw a zombie with an enchanted iron shovel and I remember hearing about it being rare. Could someone tell me how rare it is? Here is a screenshot:

It's not that unlikely. Following the wiki:

On Hard difficulty zombies have 5% chance of spawning with a tool, 1/3 of the cases it being a sword, 2/3 - a shovel, so 3.33% for a shovel.

The screenshot shows this is near a house, so Local Difficulty is increased - up to 25% chance for enchant on the tool, so 0.83%.

Now there is no table for the material of the tool, only for armor - where gold is the most common at 48.73%. I'll assume the chances for tools are similar - although there are no chainmail swords or shovels, so it's likely the chance for the shovel being golden is probably even higher. But assuming the 48.73%, the total chance would be around 0.4%. So about 1 in 250 zombies would spawn like this, and considering they are common as dirt, that's not very unique at all; comparing: chicken jockeys (baby zombies riding chickens) normally spawn in 0.25% cases.