  We consider the probabilistic description of nonrelativistic, spinless
one-particle classical mechanics, and immerse the particle in a deformed
noncommutative phase space in which position coordinates do not commute among
themselves and also with canonically conjugate momenta. With a postulated
normalized distribution function in the quantum domain, the square of the Dirac
delta density distribution in the classical case is properly realised in
noncommutative phase space and it serves as the quantum condition. With only
these inputs, we pull out the entire formalisms of noncommutative quantum
mechanics in phase space and in Hilbert space, and elegantly establish the link
between classical and quantum formalisms and between Hilbert space and phase
space formalisms of noncommutative quantum mechanics. Also, we show that the
distribution function in this case possesses 'twisted' Galilean symmetry.
