You will need a point/vector object class which can easily be written in Python. Having 3 points, p1, p2 and p3, the normal vector Nv of a plane is the cross product of the vectors p1>p2 and p1>p3. The unit vector would be:
 m = magnitude(Nv)

Point(Nv.x/m, Nv.y/m, Nv.z/m)
So the plane is now defined as a point (p1) and a unit vector. How do you know the 4th point lies on the plane?
The cross product of 2 vectors (p1 and p2):
 def cross_product(p1, p2):

'''Return the cross product of two Point object vectors. The cross product

of two vectors is a vector perpendicular to the two vectors. For

example, in an orthonormal basis, the cross product of a vector along

the X axis and a vector along the Y axis returns a vector along the Z

axis.'''

return Point(p1.y*p2.z  p1.z*p2.y,

p1.z*p2.x  p1.x*p2.z,

p1.x*p2.y  p1.y*p2.x)