There are two properties that all PDFs must satisfy. The first one is positivity (assuming that the PDF is normalized) $$ \begin{equation*} 0 \leq p(x) \leq 1. \end{equation*} $$ Naturally, it would be nonsensical for any of the values of the domain to occur with a probability greater than \( 1 \) or less than \( 0 \). Also, the PDF must be normalized. That is, all the probabilities must add up to unity. The probability of "anything" to happen is always unity. For both discrete and continuous PDFs, this condition is $$ \begin{align*} \sum_{x_i\in\mathbb D} p(x_i) & = 1,\\ \int_{x\in\mathbb D} p(x)\,dx & = 1. \end{align*} $$