P/E ratio- technical question

Hi . I have been trying to get an answer for this. But I get varying answers from people. Will appreciate your input. The comparator company has a higher PE ratio. However the volume of free-floating shares is very less since 99% of the shares are owned by a single entity. I think this factor will also contribute to a higher PE ratio as the market will be willing to pay slightly more due to the scarcity of the company share. Is this judgement correct or am I missing something. Thanks