How can the Euclidean distance be calculated with NumPy?

Use numpy.linalg.norm:

dist = numpy.linalg.norm(a-b)

This works because the Euclidean distance is the l2 norm, and the default value of the ord parameter in numpy.linalg.norm is 2. For more theory, see Introduction to Data Mining:

Use scipy.spatial.distance.euclidean:

from scipy.spatial import distance
a = (1, 2, 3)
b = (4, 5, 6)
dst = distance.euclidean(a, b)