Assume we have an observation(one point) of a line segment on a plane and the distribution of the observation is a 2D Gaussian distribution. The line in the figure is a possible line segment according to the real segment.
My question is what is the likelihood of the possible line in this case? It's that the integral of the 2D Gaussian probability density function over the line segment?
Figure: Observation and the line segment
Thank you very much in advance!