This is a quote from a cryptography book called Implementing SSL / TLS Using Cryptography and PKI By Joshua Davies.
MD5 operates on 512-bit(64 byte) blocks of input. Each block is reduced to a 128-bit(16 byte) hash. Obviously, with such a 4:1 ratio of input blocks to output blocks, there will be at least a one in four chance of a collision.
To view, the complete text with the context, please click this link.
I cannot understand how the author concludes that the probability of collision is 1/4. As far as I understand, the probability of collision would depend on the number of messages available.
If there are $2^{128} + 1$ messages or more, then the probability of collision is 1 due to pigeonhole principle. If we have only two messages, then the probability that they collide is only $1/2^{128}$. Then how does the quoted text "Obviously" make sense?
Probably the author meant that if there are $N$ messages, and the probability of a collision is $p$, with the reduction with $N$ messages the probability of a collision is $\frac{p}{4}$
Point is, as Steven Stadikni observe, this is not true.
So maybe the author is wrong (he may have overlooked the issue) but without reading the full article is not something I'm comfortable to affirm