For SHA3-512, SHA512, and Whirlpool, which algorithm has least probability for collision and preimage collision? For comparing these 3 hash functions SHA3-512, SHA512, and Whirlpool. Which one is strongest against collision and preimage attacks. Are they fundamentally the same because of the same size output? Please disregard all other characteristics of the algorithms.
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.