Arrays have a fixed size. You can't append to them. If you know the upper bounds of the array, you can preallocate the array with

np.empty((10, 10, 10))

For a 10x10x10 matrix. You can then keep 3 indices x,y,z to track the actual size you have. Eg, add a new element with:

matrix[x,y,z] = newElement
x += 1

Then when you're done, you can extract the submatrix with

finalMatrix = matrix[:x,:y,:z]

You need to use [] instead of 0 as:

n = 5
empty_list = [[[ [] for _ in range(n)] for _ in range(n)] for _ in range(n)]

Value hold by empty_list will be:

[[[[], [], [], [], []], 
  [[], [], [], [], []], 
  [[], [], [], [], []], 
  [[], [], [], [], []], 
  [[], [], [], [], []]], 
# Repeated 4 more times 

For example:

>>> empty_list[0][0][0]  # Access element with nest level 3 in list
[]

I'd suggest using np.full_like to choose the fill-value directly...

x = np.full_like((3, 1), None, dtype=object)

... of course the dtype you chose kind of defines what you mean by "empty"

You should use a list comprehension:

>>> import pprint
>>> n = 3
>>> distance = [[[0 for k in xrange(n)] for j in xrange(n)] for i in xrange(n)]
>>> pprint.pprint(distance)
[[[0, 0, 0], [0, 0, 0], [0, 0, 0]],
 [[0, 0, 0], [0, 0, 0], [0, 0, 0]],
 [[0, 0, 0], [0, 0, 0], [0, 0, 0]]]
>>> distance[0][1]
[0, 0, 0]
>>> distance[0][1][2]
0

You could have produced a data structure with a statement that looked like the one you tried, but it would have had side effects since the inner lists are copy-by-reference:

>>> distance=[[[0]*n]*n]*n
>>> pprint.pprint(distance)
[[[0, 0, 0], [0, 0, 0], [0, 0, 0]],
 [[0, 0, 0], [0, 0, 0], [0, 0, 0]],
 [[0, 0, 0], [0, 0, 0], [0, 0, 0]]]
>>> distance[0][0][0] = 1
>>> pprint.pprint(distance)
[[[1, 0, 0], [1, 0, 0], [1, 0, 0]],
 [[1, 0, 0], [1, 0, 0], [1, 0, 0]],
 [[1, 0, 0], [1, 0, 0], [1, 0, 0]]]