3. Let $[x]$ denote the greatest integer not exceeding the real number $x$. For example, $[3]=3,[\sqrt{2}]=1,[-\pi]=-4$. Let $x$ be a positive real number. If $\left[\log _{2} x\right]$ is even, then $x$ is called a lucky number. Then the probability that a number randomly selected from the interval $(0,1)$ is a lucky number is