One time pad (OTP) perfect secrecy with different key space
It cannot be perfectly secret : if $C = M \oplus K$ is your encrypted message, all the possible values of $M$ do not happen with equal probability. Indeed, the case $M = C$ (corresponding to $K = 0$) is twice less liquely to happen. You cannot have $H(M) = H(M|C)$; if e.g. $M$ is drawn uniformly at random, the distribution of $M$ given $C$ is clearly not the uniform distribution.


  What's the probability of constraints 1? If we can find also we can say that given scheme is perfectly secret or not.


The probability distribution of $M$ given $C$ is $1/2(1/2^n + 1/(2^n-1))$ for every $M \neq C$, and $1/2^{n+1}$ for $M = C$. Hence the distribution of $M$ given $C$ is clearly not uniform.