For SHA3-512, SHA512, and Whirlpool, which algorithm has least probability for collision and preimage collision?
Generic expected pre-image resistance for a hash function with $n$-bit output is  $\mathcal{O}(2^n)$ 
Generic expected collision resistance for a hash function with $n$-bit output is $\mathcal{O}(\sqrt{2^n}) = \mathcal{O}(2^{n/2})$ due to the generic birthday attack on the hash functions.


\begin{array}{|c|c|c|c|}\hline
\text{name} &amp; \text{output size} &amp;  \text{pre-image resistance} &amp; \text{collision resistance} \\ \hline
\operatorname{SHA-512} &amp; 512 &amp; \mathcal{O}(2^{512})&amp; \mathcal{O}(2^{256}) \\ \hline
\operatorname{SHA3-512} &amp; 512 &amp; \mathcal{O}(2^{512}) &amp; \mathcal{O}(2^{256}) \\ \hline
\operatorname{Whirlpool}&amp; 512 &amp;\mathcal{O}(2^{512}) &amp; \mathcal{O}(2^{256}) \\ \hline
\end{array} 

Therefore they have the same as long as there is no attack better than these on any of these.

Note 1 There is not pre-image collision. There is pre-image attack or pre-image resistance.

Note 2 SHA-512 is vulnerable to length extension attack. Prefer the SHA3-512 or Blake2 series.