Problem iterating through dictionaries

I'm trying to iterate through a source dictionary and append the value of each key to the associated key in a destination dictionary. But, for some reason it's appending the value of every key in the source dictionary to each key in the destination dictionary:

source = dict.fromkeys(range(3), 1)
dest = dict.fromkeys(range(3), [])

for key in source:
    dest[key].append(source[key])

>>> print(dest)
expected: {0: [1], 1: [1], 2: [1]}
actual: {0: [1, 1, 1], 1: [1, 1, 1], 2: [1, 1, 1]}

This is happening both in version 3.7 and 3.4, and how I loop doesn't seem to matter: I can use a while loop and the same thing happens, I can structure the for loop as for key, value in source.items():, I can copy the values in source to a list and then try to append them one at a time into dest and it still ends up the same way. No matter what I do, it acts like a nested loop and appends every value from source into each key of dest even though I'm not telling it to do anything like that.

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What am I doing wrong?