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I am trying to model a distribution, on the number of occurrences of an event in a 24 hour time span.

Right now, I discretize the 24 hour time span into hourly intervals, and each hour is taken as a categorical outcome, and I count the number of occurrences of the event in each hour (outcome). Hence, this problem is modeled as a multinomial distribution.

As time is a continuous variable, is there a continuous version of multinomial distribution? That is, I can count the number of occurrence of the event in the continuous outcome(time).

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Why a multinomial distribution? Is there a fixed total number of occurances? The logical model to use would be a Poisson process. Anyway, the continuous analogue of the multinomial distribution is the multivariate normal distribution. – Raskolnikov Mar 2 '12 at 22:32

A similar distribution would be the Dirichlet distribution.

A random sample of a Dirichlet distribution is a set of probabilities that add to one. You can then multiply each by, say, $24$, to get a "continuous multinomial distribution."
This is just a direct answer to your question about "continuous multinomial distribution", whether you should use it to model your data is another question.

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