Depends on how random your choice of tile was. If it was completely random then you have a 29% chance (ish) of being next to a diamond, if it was not random and you only picked tiles in the middle of the board then you have about a 42% chance of being next to a diamond. The chance of getting all 4 in a row then ranges from 0.7% to 3.1%. So unlikely but certainly not impossible.

(Disclaimer: all back-of-an-envelope calculations so I might be wrong)

*Edit: Seems my maths is a bit off after building a quick simulation (1,000,000 sims). My probabilities above are conditional on you not getting the diamond. The unconditional probabilities are 27.5% and 40% respectively leading to the final range being 0.6% to 2.6%.*