There is a 2 in 2^64 (±0; 1 in 2^63) chance of drawing a double-precision zero from a random pattern of bits (there are invalid bit patterns, including ±infinity and a variety of forms of Not a Number patterns that were included in the "non-singular" 1x1 matrix, which is arguably a good way of putting it).

So drawing 4 random bit patterns would give you a space of (2^64)^4 = 2^256 possible double-precision numbers....