First impressions often dictate whether a customer will visit your booth or not at a trade show, and by creating an eye-catching booth you will instantly increase your opportunity of having a successful show.
想请教，介词of后为何要用动名词having, 为何不能直接是a successful show?
increase your opportunity of having a successful show：
没having，opportunity 和show 就没任何关联性。加了having 表达一个“动宾事件”。意为“获得成功演出的（机会）”。
除此之外，大家把of having 转换为不定式，就应该好懂了：
increase your opportunity tohave a successful show
your opportunity to do sth. 你做某事的机会。没了“做”，意义不完整。