We're starting with a probability space $(\Omega,\mathcal F,\mathbb P)$. We have the process $V_t=V_oe^{(\mu-\delta)t+\sigma W_t}$, where $W_t$ is a standard Brownian motion. Having the shift operator given as: $$\forall\omega\in\Omega\quad\Theta_{t}(\omega)(s)=\omega(s+t)-\omega(t),\,s\geq0$$ where $\omega$ is path of a Brownian motion, such that for a stochastic process X we have $$X_{s}(\Theta_{t}(\omega))=X_{t+s}(\omega).$$ Now there should be defined a new probability space and a probability measure on that space such that $\mathbb Q_{t,x}(V_t=x)=1$. How should the new probability space and a probability measure $\mathbb Q_{t,x}$ be defined?
I'm aware that it cannot be defined as simply conditional probability since the condition would be of measure $0$.
Thank you for your help!!